A  SHORT  HISTORY  OF  SCIENCE 


The  whole  of  modern  thought  is  steeped  in  science.  .  . . 
The  greatest  intellectual  revolution  mankind  has  yet 
seen  is  now  slowly  taking  place  by  her  agency. 

—  HUXLEY. 

The  history  of  science  familiarizes  us  with  the  ideas 
of  evolution  and  the  continuous  transformation  of  hu- 
man things.  ...  It  shows  us  that  if  the  accomplish- 
ments of  mankind  as  a  whole  are  grand  the  contribu- 
tion of  each  is  small.  _  SARTON> 

The  history  of  science  is  the  real  history  of  mankind. 

—  Du  Bois  REYMOND. 

The  history  of  science  .  .  .  presents  science  as  the 
constant  pursuit  of  truth  ...  a  growth  to  which  each 
may  contribute.  .  .  .  Science  is  international. 

—  LlBBY. 


SHORT  HISTORY  OF  SCIENCE 


BY 
W.   T.   SEDGWICK  AND  H.   W.   TYLER 

Professor  of  Biology  Professor  of  Mathematics 

at  the 

Massachusetts  Institute  of  Technology 
Cambridge 


The  history  of  science  should  be 
the  leading  thread  in  the  history  of  civilization. 

—  SARTON. 


t*  •* 


Nefo  ff  orfc 

THE   MACMILLAN   COMPANY 
1917 

All  rights  reserved 


COPYRIGHT,  1917, 
BY  THE  MACMILLAN  COMPANY. 


Set  up  and  electrotyped.     Published  November,  1917. 


J.  8.  Gushing  Co.  —  Berwick  &  Smith  Co. 
Norwood,  Mass.,  U.S.A. 


PREFACE 

THIS  book  is  the  outgrowth  of  a  lecture  course  given  by  the 
authors  for  several  years*  to  undergraduate  classes  of  the  Massa- 
chusetts Institute  of  Technology,  the  chief  aims  of  the  course 
being  to  furnish  a  broad  general  perspective  of  the  evolution  of 
science,  to  broaden  and  deepen  the  range  of  the  students'  interests 
and  to  encourage  the  practice  of  discriminating  scientific  reading. 

There  are  of  course  excellent  treatises  on  the  history  of  partic- 
ular sciences,  but  these  are  as  a  rule  addressed  to  specialists,  and 
concern  themselves  but  little  with  the  important  relations  of  the 
sciences  one  to  another  or  to  the  general  progress  of  civilization. 
The  present  work  aims  to  furnish  the  student  and  the  general 
reader  with  a  concise  account  of  the  origin  of  that  scientific  knowl- 
edge and  that  scientific  method  which,  especially  within  the  last 
century,  have  come  to  have  so  important  a  share  in  shaping  the 
conditions  and  directing  the  activities  of  human  life.  The 
specialist  in  any  branch  of  science  is  finding  it  more  and  more 
difficult  to  keep  himself  informed,  even  to  the  indispensable  mini- 
mum extent,  as  to  current  progress  in  his  own  field,  —  and  hence 
his  frequent  neglect  of  all  other  branches  than  his  own. 

It  may  reasonably  be  expected  that  some  attention  to  the  his- 
tory of  science  on  the  part  of  students  will  give  them  a  better 
understanding  of  the  broad  tendencies  which  have  determined  the 
general  course  of  scientific  progress,  will  enlarge  their  apprecia- 
tion of  the  work  of  successive  generations,  and  tend  to  guard  them 
against  falling  into  those  ancient  pitfalls  which  have  bordered 
the  paths  of  progress.  In  the  words  of  Mach :  — 

There  is  no  grander  nor  more  intellectually  elevating  spectacle  than  that 
of  the  utterances  of  the  fundamental  investigators  in  their  gigantic  power. 

*  By  the  senior  author  since  1889. 
v 

S* 

367772 


vi  PREFACE 

Possessed  as  yet  of  no  methods  —  for  these  were  first  created  by  their  labors 
and  are  only  rendered  comprehensible  to  us  by  their  performances  —  they 
grapple  with  and  subjugate  the  object  of  their  inquiry  and  imprint  upon  it 
the  forms  of  conceptual  thought.  Those  who  know  the  entire  course  of  the 
development  of  science  will . . .  judge  more  freely  and  more  correctly  the  sig- 
nificance of  any  present  scientific  movement  than  those  who,  limited  in  their 
views  to  the  age  in  which  their  own  lives  have  been  spent,  contemplate  merely 
the  trend  of  intellectual  events  at  the  present  moment. 

At  a  time  when  the  forces  of  science  are  being  diverted  from  the 
promotion  and  conservation  of  civilization  to  its  destruction,  and 
when  attempts  are  being  made  to  turn  the  waters  now  flowing 
in  the  stream  of  science  back  into  ancient  and  so-called  classical 
channels,  it  will  be  well  for  the  general  reader  no  less  than  the 
student  of  science  to  review  its  history,  and  to  judge  for  himself 
concerning  its  proper  place  in  contemporary  life  and  education. 
Many  volumes  would  be  required  to  depict  the  lives  of  the  workers, 
-  often  marked  by  self-denial  and  sometimes  by  persecution,  - 
to  trace  the  full  significance  of  their  achievements,  or  to  portray 
the  spirit  animating  their  labors ;  —  that  spirit  of  science  to  which, 
regarding  it  as  a  critic  rather  than  a  votary,  impressive  tribute 
has  been  paid  by  one  of  our  modern  seers :  — 

A  greater  gain  to  the  world  .  .  .  than  all  the  growth  of  scientific  knowl- 
edge is  the  growth  of  the  scientific  spirit,  with  its  courage  and  serenity,  its 
disciplined  conscience,  its  intellectual  morality,  its  habitual  response  to  any 
disclosure  of  the  truth. 

—  F.  G.  Peabody. 

It  has  naturally  been  foreign  to  the  purpose  of  the  authors  to 
admit  matter  too  technical  for  the  general  student  or,  on  the  other 
hand,  too  slight  in  its  influence  on  the  general  progress  of  science. 
The  division  of  responsibility  between  them  corresponds  roughly 
to  that  implied  by  the  title  "mathematical"  and  "natural 
sciences",  and  emphasis  has  been  laid  on  interrelations  rather 
than  on  distinctions  between  the  various  sciences.  The  mathe- 
matical group  from  their  relatively  greater  age  and  higher  de- 
velopment afford  the  best  examples  of  maturity;  the  natural 
sciences  illustrate  more  clearly  recent  progress.  No  attempt 


PREFACE  vii 

has  been  made  by  the  authors  to  follow  an  encyclopaedic  plan,  under 
which  all  fields  should  receive  proportional  space  and  treatment, 
each  by  a  competent  representative,  but  some  fullness  of  presenta- 
tion has  been  aimed  at  in  the  particular  branches  with  which  they 
are  themselves  familiar,  with  briefer  indication  of  developments 
along  other  lines. 

The  authors  gladly  acknowledge  their  indebtedness  to  mafty 
men  of  science  interested  in  their  undertaking,  and  to  the  special 
histories  already  referred  to,  on  which  their  own  work  is  largely 
based.  Many  brief  typical  quotations  from  the  more  important 
authorities  are  given  as  a  basis  for  wider  or  more  special  study, 
but  no  systematic  attempt  has  been  made  to  examine  original 
sources.  No  one  can  possibly  be  more  aware  than  are  the  authors 
of  the  shortcomings  of  their  work,  and  corrections  of  errors,  from 
which  a  book  of  this  kind  cannot  hope  to  have  escaped,  will  be 
welcomed. 

MASSACHUSETTS  INSTITUTE  OF  TECHNOLOGY, 
CAMBRIDGE,  1917. 


TABLE  OF  CONTENTS 

CHAPTER  I 

PAGE 

EARLY  CIVILIZATIONS 1 

The  Antiquity  and  Ancestry  of  Man — Archasology — Prehis- 
toric Man  —  The  Science  of  Mankind,  Anthropology  —  Primi- 
tive Interpretations  of  Nature  —  Prevalence  of  Animism  in 
Antiquity  —  Sources  of  Information  Concerning  Prehistoric  and 
Ancient  Times  —  Some  Ancient  Lands"  and  Peoples  —  Babylo- 
nia and  Assyria  —  Egypt  —  Phoenicia  —  The  Hebrews  —  The 
Emergence  of  European  Civilization  —  Mge&n  Civilization  in 
the  Bronze  Age  —  The  Iron  Age ;  The  Greeks  or  Hellenes. 

CHAPTER  II 
EARLY  MATHEMATICAL  SCIENCE  IN  BABYLONIA  AND  EGYPT     .        .      20 

Primitive  Astronomical  Notions  —  The  Planets  —  Astrology 
and  Cosmology  —  Primitive  Counting  —  Primitive  Geometry  — 
Relation  of  Greek  to  Older  Civilizations  —  Babylonian  Arith- 
metic —  Babylonian  Astronomy  —  Babylonian  Geometry  — 
Mathematical  Science  in  Egypt  —  The  Ahmes  Papyrus  —  Egyp- 
tian Land  Measurement  —  Egyptian  Geometry. 

CHAPTER  III 

THE  BEGINNINGS  OP  SCIENCE       .        .        *       ...      •       •        •      35 

Geographical  Boundaries  —  Indebtedness  of  Greece  to  Baby- 
lonia and  Egypt  —  The  Greek  Point  of  View  —  Sources  —  The 
Calendar  —  Time  Measurement  —  Greek  Arithmetic  —  Greek 
Geometry  —  The  Ionian  Philosophers  —  Thales  —  Milesian  Cos- 
mology —  Anaximander  —  Anaximenes  —  Pythagoras  and  his 
School  —  Pythagorean  Arithmetic  —  Pythagorean  Geometry  — 
Pythagorean  Physical  Science  —  Terrestrial  Motion :  Philolaus, 
Hicetas. 

CHAPTER   IV 

SCIENCE  IN  THE  GOLDEN  AGE  OF  GREECE 58 

Literature  and  Art  —  Parmenides — Empedocles — Anaxagoras 
—  The  Atomists  —  Democritus  of  Abdera  —  The  Beginnings  of 

ix 


TABLE   OF   CONTENTS 

PAGE 

Rational  Medicine :  Hippocrates  of  Cos  —  The  Sophists  —  Hip- 
pias  of  Elis  —  The  Criticism  of  Zeno  —  Circle  Measurement : 
Antiphon  and  Bryson,  Hippocrates  of  Chios  —  Plato  and  the 
Academy  —  The  Analytic  Method  —  Platonic  Cosmology  — 
Archytas  —  Mensechmus :  Conic  Sections  —  A  New  Cosmology : 
Eudoxus  —  Aristotle  —  Aristotle's  Mechanics  —  Aristotelian 
Astronomy  —  Theophrastus — Epicurus  and  Epicureanism  — 
Heraclides :  Rotation  of  the  Earth. 


CHAPTER  V 

GREEK  SCIENCE  IN  ALEXANDRIA  .        . 87 

The  Museum  at  Alexandria  —  Euclid  —  Euclid's   Elements 

—  Influence  of  Euclid  — .Criticism  of  Euclid  —  Other  Works  of 
Euclid  —  Archimedes  —  Archimedes  and  Euclid  —  Circle  Meas- 
urement —  Quadrature  of  the  Parabola  —  Spirals  —  Sphere  and 
Cylinder  —  Mechanics  of  Archimedes  —  Archimedes  as  an  En- 
gineer —  Alexandrian  Geography ;  Earth  Measurement  —  Era- 
tosthenes —  Apollonius  of  Perga  —  Apollonius  and  Archimedes  — 
Medical  Science  at  Alexandria ;  Beginnings  of  Human  Anatomy.  . 

CHAPTER  VI 

THE  DECLINE  OP  ALEXANDRIAN  SCIENCE 115 

Orbital  Motion  of  the  Earth :  Aristarchus  —  Excentric  Cir- 
cular Orbits  —  Epicycles  —  Hipparchus :  Star  Catalogue  —  Pre- 
cession of  the  Equinoxes  —  Other  Astronomical  Discoveries ; 
Planetary  Theory  —  Invention  of  Trigonometry  —  Inventions : 
Ctesibus  and  Hero  —  Hero's  Triangle  Formula  —  Inductive 
Arithmetic:  Nicomachus  —  Ptolemy  and  the  Ptolemaic  Sys- 
tem —  The  Almagest  —  Other  Works  of  Ptolemy  —  Pappus  — 
Beginnings  of  Algebra :  Diophantus  —  Conclusion  and  Retrospect. 

CHAPTER  VII 
THE  ROMAN  WORLD.     THE  DARK  AGES     .        .    ,   .  T  ..        •        •    141 

The  Roman  World-Empire  —  The  Roman  Attitude  towards 
Science  —  Roman  Engineering  and  Architecture  —  Slave  Labor 
in  Antiquity  —  Julius  Caesar  and  the  Julian  Calendar  —  Vitru- 
vius  on  Architecture  —  Frontinus  on  the  Waterworks  of  Rome 

—  Roman  Natural  Science  and  Medicine  —  Lucretius  —  Strabo 

—  Pliny  the  Elder  —  Galen  —  Late  Roman  Mathematical  Sci- 
ence—  Capella  —  Boethius  —  Science  and  the  Early  Christian 
Church  —  The  Eastern  Empire ;  Edict  of  Justinian  —  The  Dark 
Ages  —  The  Establishment  of  Schools  by  Charlemagne. 


TABLE    OF   CONTENTS  xi 

CHAPTER  VIII 

.  PAGE 

HINDU  AND  ARABIAN  SCIENCE.     THE  MOORS  IN  SPAIN  .        .        .    156 

Alexandria  —  Hindu  Mathematics  —  Hindu  Astronomy  — 
Mohammed  and  the  Hegira  —  Arabian  Mathematical  Science 

—  Arabian  Astronomy  —  Asiatic  Observatories  —  The  Moors  in 
Spain. 

CHAPTER   IX 
PROGRESS  OF  SCIENCE  TO  1450  A.D.     .......     172 

The  Crusades  —  Trivium  and  Quadrivium ;  Scholasticism  — 
Medieval  Universities  —  Transmission  of  Science  through  - 
Moorish  Spain  —  Dawn  of  the  Renaissance  —  Mathematical 
Science  in  the  Thirteenth  Century  —  Roger  Bacon  —  Dante 
Alighieri  —  Computation  in  the  Middle  Ages  —  Mathematics 
in  the  Medieval  Universities  —  The  Renaissance  —  Humanism 

—  Alchemy  —  The  Mariner's  Compass  —  Clocks  —  Wool  and  - 
Silk ;  Textiles  in  the  Middle  Ages  —  The  Invention  of  Printing. 

CHAPTER  X 

A  NEW  ASTRONOMY  AND  THE  BEGINNINGS  OP  MODERN  NATURAL 

SCIENCE      ............     191 

The  Age  of  Discovery  —  The  Reformation  —  Pioneers  of  the 
New  Astronomy  —  Conditions  Necessary  for  Progress  —  Nico- 
laus  Copernicus  —  De  Revolutionibus  —  Influence  of  Copernicus 

—  Tycho  Brahe  —  Uraniborg  —  Kepler  —  Galileo  —  Medical  and 
Chemical  Sciences  —  Anatomy:  Vesalius  —  Revival  of  Interest 
in  Natural  History. 

CHAPTER  XI 

PROGRESS  OF  MATHEMATICS  AND  MECHANICS  IN  THE  SIXTEENTH 

CENTURY    .        .        .        ...       .       .        .        .        .        .230 

Aims  and  Tendencies  of  Mathematical  Progress  —  Pacioli  — 
Geometry  in  Art  —  Robert  Recorde  —  Algebraic  Equations  of 
Higher  Degree  —  Tartaglia,  Cardan  —  Symbolic  Algebra  :  Vieta 

—  Development  of  Trigonometry  —  Map-making  —  The  Grego- 
rian Calendar  —  A  New  Invention  for  Computation  —  "Two 
New  Branches  of  Science  "  —  A  Pioneer  in  Mechanics ;  Stevinus 

—  Giordano  Bruno. 

CHAPTER  XII 

NATURAL  AND  PHYSICAL  SCIENCE  IN  THE  SEVENTEENTH  CENTURY    255 

The  Circulation  of  the  Blood :  Harvey  —  Atmospheric  Pres- 
sure; Torricelli's  Barometer  —  Further  Studies  of  the  Atmos- 


xii  TABLE   OF   CONTENTS 

PAGE 

phere;  Gases  —  From  Philosophy  to  Experimentation  —  From 
Alchemy  to  Chemistry  —  A  False  Theory  of  Combustion ; 
Phlogiston  —  Beginnings  of  Organic  Chemistry  —  Organization 
of  the  First  Scientific  Academies  and  Societies  —  The  New 
Philosophy:  Bacon  and  Descartes  —  Progress  of  Natural  and 
Physical  Science  in  the  Seventeenth  Century. 


CHAPTER  XIII 

BEGINNINGS  OP  MODERN  MATHEMATICAL  SCIENCE    ....    273 

Mathematical  Philosophy;  Analytic  Geometry:  Descartes 
—  Indivisibles:  Cavalieri  —  Protective  Geometry  :  Desargues  — 
Theory  of  Numbers  and  Probability :  Fermat,  Pascal  —  Me- 
chanics and  Optics:  Huygens  —  Wallis  and  Barrow  —  Isaac 
Newton  —  Optics  —  The  Theory  of  Gravitation;  Principia  — 
Newton's  Mathematics ;  Fluxions  —  Leibnitz  —  Halley  :  Pre- 
diction of  Comets. 


CHAPTER  XIV 

NATURAL  AND  PHYSICAL  SCIENCE  IN  THE  EIGHTEENTH  CENTURY    304 

Chemistry;  Decline  of  the  Phlogiston  Theory  —  A  New 
Chemistry :  Priestley  and  Lavoisier  —  The  Synthesis  of  Water 

—  Beginnings  of  Modern  Ideas  of  Sound  —  The  Beginnings  of 
Modern  Ideas  of  Heat ;  Latent  and  Specific  Heat,  Calorimetry 

—  Eighteenth  Century  Researches  on  Light  —  Beginnings  of 
Modern  Ideas  of  Electricity  and  Magnetism — Beginnings  of 
Modern  Ideas  of   the    Earth  —  Eighteenth   Century  Progress 
in  Botany,  Zoology,  etc.  —  Progress  in  Comparative  Anatomy 
and    Physiology  —  The    Industrial    Revolution;     Inventions; 
Power  —  Influence  of  Science  upon  the  Spirit  of  the  Eighteenth 
Century. 

CHAPTER  XV 

MODERN  TENDENCIES  IN  MATHEMATICAL  SCIENCE  ....    323 

Mathematics  and  Mechanics  in  the  Eighteenth  Century  — 
Progress  in  Theoretical  Mechanics  —  Celestial  Mechanics  — 
The  Perturbation  Problem  —  The  Nebular  Hypothesis  —  Mod- 
ern Astronomy;  Telescopic  Discoveries  —  Mathematical  Prog- 
ress and  Physical  Science  —  Nineteenth  Century  Mathematics 

—  Non-Euclidean  Geometry  —  Imaginary  Numbers  —  The  Dis- 
covery of  Neptune  —  Cosmic  Evolution  —  Distance  of  the  Stars 

—  Mathematical  Physics. 


TABLE    OF   CONTENTS  xiii 


CHAPTER  XVI 

PAOE 

SOME  ADVANCES  IN  PHYSICAL  SCIENCE  IN  THE  NINETEENTH  CEN- 
TURY.   ENERGY  AND  THE  CONSERVATION  OF  ENERGY        .        .    348 

Modern  Physics  —  Heat,  Thermometry  :  Carnot,  Rumford  — 
Light;  Wave  Theory,  Velocity:  Young,  Fresnel  —  The  Spec- 
troscope and  Spectrum  Analysis  —  Electricity  and  Magnetism : 
Faraday,  Green,  Ampere,  Maxwell  —  Electromagnetic  Theory 
of  Light  —  Kinetic  Theory  of  Gases:  Clausius  —  The  Concep- 
tion of  Energy  —  Dissipation  of  Energy  —  Modern  Chemistry 

—  Chemical    Laboratories :    Liebig  —  Quantitative    Relations ; 
Atoms,  Molecules,  Valence  —  Synthesis  of  Organic  Substances 

—  A  Periodic  Law  among  the  Elements  —  Chemical  Structure 

—  Physical  Chemistry;   Electrolytic  and  Thermodynamic  De- 
velopments of  Chemistry. 


CHAPTER  XVII 

SOME  ADVANCES  IN  NATURAL  SCIENCE  IN  THE  NINETEENTH  CEN- 
TURY.   COSMOGONY  AND  EVOLUTION 366 

Influence  of  Eighteenth  Century  Revolutions  —  The  Scientific 
Revolution  —  Effects  of  the  Rapid  Increase  of  Knowledge  — 
Gradual  Appreciation  of  the  Permanence  and  Scope  of  Natural 
Law  —  Natural  Theology  and  an  Age  of  Reason  —  Natural  Phi- 
losophy and  Natural  History ;  Differentiation  and  Hybridizing 
of  the  Sciences  —  Progress  in  Zoology  —  Progress  in  Botany  — 
Progress  in  Microscopy;  the  Achromatic  Objective  —  Embry- 
ology —  Progress  in  Physiology :  Johannes  Miiller ;  Claude  Ber- 
nard —  Pathology  before  Pasteur  —  The  Germ  Theory  of 
Fermentation,  Putrefaction  and  Disease :  Pasteur  —  Antiseptic 
and  Aseptic  Surgery :  Lister  —  Rise  of  Bacteriology  and  Para- 
sitology  —  Biogenesis  versus  Spontaneous  Generation  —  Prog- 
ress of  Geological  Science  —  Glaciers  and  Glacial  Theories  — 
Rise  of  Palaeontology  —  Ancient  and  Modern  Theories  of  Cos- 
mogony—  Relationship  of  the  Heavens  and  the  Earth  —  The 
Scale  of  Life  and  the  Phases  of  Life  —  General  Resemblance  of 
Man  to  the  Lower  Animals  —  Anatomical  and  Microscopical 
Similarity  of  Animals  and  Plants ;  Organs,  Tissues,  Cells  and 
Protoplasms  —  Fundamental  Unity  of  Nature;  Organic  versus 
Inorganic  World  —  Treviranus'  Biology  and  Lamarck's  Zoologi- 
cal Philosophy  —  Voyages  and  Explorations  of  Naturalists  — 
Darwin's  Origin  of  Species  —  His  Descent  of  Man  —  Decline 
of  the  Theory  of  Special  Creation  —  Influence  of  an  Age  of 
Invention  and  Industry  —  Science  in  the  Dawn  of  the  Twen- 
tieth Century. 


xiv  TABLE    OF   CONTENTS 

APPENDICES 

PAGE 

A.  The  Oath  of  Hippocrates  (about  400  B.C.)         .         .         .    399 

B.  The  OpusMajus  of  Roger  Bacon  (1267  A.D.).    An  Anal- 
ysis of  the  Sixth  Part  by  J.  H.  Bridges 400 

C.  Dedication  of  The  Revolutions  of  the  Heavenly  Bodies 

by  Nicolas  Copernicus  (1543) 407 

D.  William  Harvey's  Dedication  of  his  Work  on  the  Circu- 
lation of  the  Blood  (1628)  .        . 412 

E.  Galileo  before  the  Inquisition  (1633)  ....     414 

F.  Preface   to    the   Philosophies   Naturalis  Principia  Mathe- 
matica,  by  Isaac  Newton  (1686)  .    \- 420 

G.  An  Inquiry  into  the  Causes  and  Effects  of  the  Variolce 
Vaccines,  by  Edward  Jenner  (1798) 422 

H.   Principles  of  Geology,  by  Charles  Lyell  (1830) .         .         .429 
I.  SOME   INVENTIONS  OF  THE  EIGHTEENTH  AND  NINETEENTH 

CENTURIES 438 

Power ;  Its  Sources  and  Significance  -. —  Gunpowder,  Nitro- 
glycerine, Dynamite  —  The  Steam-Engine  —  The  Spinning 
Jenny,  the  Water  Frame,  and  the  Mule  —  The  Cotton  Gin 

—  Steam  Transportation  —  The  Achromatic  Compound  Micro- 
scope —  Illuminating  Gas  —  Friction  Matches  —  The  Sewing- 
Machine —  Photography  —  Anaesthesia;   The   Ophthalmoscope 

—  India-Rubber  —  Electrical  Apparatus ;  Telegraph,  Telephone, 
Electric  Lighting,  Electric  Machinery  —  Food   Preserving  by 
Canning  and  Refrigeration  —  The  Internal-Combustion  Engine 

—  Aniline  —  The  Manufacture  of  Steel :  Bessemer  —  Agricultu- 
ral Apparatus  and  Inventions  —  Applied  Science ;  Engineering. 

A  TABLE  OF  IMPORTANT  DATES  IN  THE  HISTORY  OF  SCIENCE  AND 

CIVILIZATION 449 

A  SHORT  LIST  OF  BOOKS  OF  REFERENCE 459 

INDEX 469 


ILLUSTRATIONS 

PAGE 

Hecatgeus'  Map  of  the  World,  517  B.C 34 

Herodotus' Map  of  the  Worl  ]          .        . 57 

Behaim's  Globe,  1492  A.D 190 

The  Copernican  System 198 

Tycho  Brahe's  Quadrant opposite  204 

Uraniborg opposite  206 

Kepler                         opposite  210 

Galileo                        opposite  217 

Galileo's  Dialogue .        .        .   opposite  224 

Stevinus'  Triangle 252 

Huygens                     opposite  286 

Huygens'  Clock opposite  288 

Newton's  Telescope  and  Newton's  Theory  of  the  Rainbow    opposite  292 
Sketch  Map  of  Places  Important  in  Ancient  and  Medieval 

Science opposite  448 


xv 


A   SHORT   HISTORY   OF  SCIENCE 


CHAPTER  I 
EARLY   CIVILIZATIONS 

'The  night  of  time  far  surpasseth  the  day'  said  Sir  Thomas 
Browne ;  and  it  is  the  task  of  Archaeology  to  light  up  some  parts  of 
this  long  night.  —  Charles  Eliot  Norton. 

THE  ANTIQUITY  AND  ANCESTRY  OF  MAN.  —  It  is  now  gen- 
erally agreed  that  men  of  some  sort  have  been  living  upon  this 
earth  for  many  thousand  years.  It  is  also,  though  perhaps  less 
generally,  agreed  that  mankind  has  descended  from  the  lower 
animals,  precisely  as  the  men  of  to-day  have  descended  from 
men  that  lived  and  died  ages  ago. 

The  history  of  science,  however,  is  not  so  much  concerned  with 
the  ancestry  or  origin  of  mankind  as  with  its  antiquity ;  for  while 
science  is  a  comparatively  recent  achievement  of  the  human  race, 
its  roots  may  be  traced  far  back  in  practices  and  processes  of  pre- 
historic and  primitive  times.  Mankind  is  very  old,  but  science 
so  far  as  we  know  had  no  existence  before  the  beginning  of 
history,  i.e.  about  6000  years  ago,  and  until  2500  years  ago  it 
occurred  if  at  all  only  in  rudimentary  form.  The  best  opinion 
of  to-day  holds  that  man  has  been  on  this  earth  at  least  250,000 
years,  and  in  spite  of  wide  variations  is  of  one  zoological  "  kind  " 
or  "  species  "  and  three  principal  types  or  "  races/'  viz.,  white  or 
Caucasian,  yellow  or  Mongolian,  and  black  or  Ethiopian  (Negroid). 
These  great  races  are  believed  to  have  had  a  common  ancestry 
in  a  more  primitive  race,  and  this  in  turn  to  have  descended  from 
the  lower  animals.  It  is  furthermore  held  that  there  was  prob- 


2        A  i:t.-:.  A;  -SHORT  .HISTORY   OF   SCIENCE 

ably  one  principal  place  of  origin,  or  "  cradle,"  of  the  human 
race  from  which  have  spread  all  known  varieties  of  mankind,  alive 
or  extinct,  and  that  this  was  probably  in  "Indo-Malaysia"  in 
that  remarkable  valley  which  lies  between  the  rivers  Tigris  and 
Euphrates  and  in  its  upper  part  is  known  as  Mesopotamia  (be- 
tween the  rivers). 

Mesopotamia,  or  the  broad  valley  of  the  Tigris  and  Euphrates, 
was  the  cradle  of  civilization  in  the  remotest  antiquity.  There  can 
be  little  doubt  that  man  evolved  somewhere  in  southern  Asia,  possibly 
during  the  Pleiocene  or  Miocene  times  ....  [And]  as  paleolithic  man 
was  certainly  interglacial  in  Europe,  we  may  assume  that  he  was 
preglacial  in  Asia.  .  .  . 

The  earliest  known  civilization  in  the  world  arose  north  of  the 
Persian  Gulf  among  the  Sumerians  ....  but  the  Babylonians  of 
history  were  a  mixed  people,  for  Semitic  influences  according  to 
Winckler  began  to  flow  up  the  Euphrates  Valley  from  Arabia  during 
the  fourth  millennium  B.C.  This  influence  was  more  strongly  felt, 
however,  in  Akkad  than  in  Sumer,  and  it  was  in  the  north  that  the 
first  Semitic  Empire,  that  of  Sargon  the  Elder  (about  2500  B.C. 
according  to  E.  Meyer)  had  its  seat.  .  .  .  The  supremacy  of  Babylon 
was  first  established  by  the  Dynasty  of  Hamurabi  (about  1950  B.C., 
earlier  according  to  Winckler)  which  was  overthrown  by  the  Hittites 
about  1760  B.C.  Then  followed  the  Kassite  dominion,  which  lasted 
from  about  1760  to  1100  B.C.  ...  It  was  probably  due  to  them  that 
the  horse,  first  introduced  by  the  Aryans,  became  common  in  south- 
west Asia;  it  was  introduced  into  Babylon  about  1900  B.C.  but 
was  unknown  in  Hamurabi's  reign.  —  Haddon. 

ARCHAEOLOGY.  —  The  study  of  antiquity,  and  especially  of 
prehistoric  antiquity,  is  known  as  archaeology  (the  science  of 
antiquities  or  beginnings),  and  is  based  upon  finds  of  ruins, 
tools,  weapons,  caves,  skeletons,  carvings,  ornaments,  and 
similar  remains  or  evidences  of  human  life  and  action  in  pre- 
historic times.  It  has  been  well  described  as  "unwritten history." 
Remains  of  all  kinds  have  long  been  roughly  but  conveniently 
classified  into  three  groups  corresponding  to  three  periods  of 
development,  viz. :  a  Stone  Age,  a  Bronze  Age,  and  an 


EARLY   CIVILIZATIONS  3 

Iron  Age,  according  to  the  use  of  stone,  bronze  and  iron 
implements. 

PREHISTORIC  MAN.  —  If  therefore  we  would  begin  the  history 
of  science  at  the  very  beginning,  we  must  turn  far  backward  in 
imagination  to  a  time  when  the  human  race  was  barely  superior 
to  the  beasts  that  perish.  Absorbed  in  a  fierce  struggle  for  exist- 
ence, the  passing  generations  had  little  history  and  left  behind 
them  no  permanent  records.  In  one  respect  nevertheless  mankind 
stood  far  above  the  beasts;  namely,  in  possessing  the  power  of 
language,  by  which  they  could  not  only  communicate  more  readily 
one  with  another,  but  also  convey  to  their  descendants  through 
oral  tradition  something  of  whatever  they  might  possess  of  accu- 
mulated knowledge.  Eventually,  though  slowly,  the  generations 
began  to  leave  behind  them  more  enduring  records,  —  at  first 
crude  and  fragmentary,  in  the  form  of  tools,  cairns,  and  other 
monuments,  or  in  drawings,  paintings,  or  carvings,  on  ivory  or 
rocks  or  trees,  or  on  the  walls  of  caverns,  —  which  should  serve 
to  inform  or  instruct  other  men.  Finally,  but  still  slowly,  and 
especially  out  of  this  so-called  "picture-writing,"  grew  the  art  of 
writing,  which  furnished  a  means  of  keeping  permanent  records 
of  the  past  and  a  new  and  more  perfect  way  of  communication 
between  living  men  and  races  of  men.  We  who  have  ourselves 
witnessed  some  of  the  consequences  of  improvements  in  the  arts 
of  communication  between  men  and  nations,  such  as  have  recently 
been  effected  by  steam  transportation  and  telegraphy  and  teleph- 
ony, can  to  some  extent  realize  how  much  the  introduction  of  the 
rudiments  of  the  art  of  writing  may  have  meant  in  the  progress  of 
prehistoric  and  primitive  mankind. 

THE  SCIENCE  OF  MANKIND.  ANTHROPOLOGY.  —  The  various 
steps  in  the  evolution  of  mankind  and  in  the  earliest  development 
of  civilization  and  the  arts  form  the  subject  matter  of  one  of  the 
youngest  of  the  sciences,  anthropology,  to  works  upon  which 
the  reader  is  referred  who  would  pursue  these  matters  further. 
One  of  the  earliest  and  still  one  of  the  most  interesting  of  these, 
Man's  Place  in  Nature,  by  Huxley,  is  now  a  classic.  Another, 
also  somewhat  out  of  date  but  still  very  valuable,  entitled 


4  A   SHORT   HISTORY    OF   SCIENCE 

"  Anthropology/'  is  of  special  interest  because  its  author,  E.  B. 
Tylor,  was  the  founder  of  the  science  and  is  still  living  (in  1916).1 

THE  CHILDHOOD  OF  THE  RACE.  —  There  is  reason  to  believe 
that  the  human  race,  in  its  long  and  slow  development,  has  passed 
through  periods  of  essential  childhood  and  youth,  very  much  as 
the  individual  human  being  passes  slowly  through  infancy  onwards ; 
and  that,  precisely  as  the  individual  begins  his  intellectual  life  in 
wonder,  questioning,  and  curiosity,  so  the  race  has  advanced  from 
a  condition  of  childish  wonder,  questionings,  and  interpretations  of 
mankind  and  the  external  world,  —  sun,  moon,  and  stars,  thunder 
and  lightning,  wind,  rain,  and  snow,  —  which  have  gradually 
developed  into  more  mature  and  more  scientific  explanations. 
This  principle  of  an  essential  parallelism  between  individual 
development  and  racial,  named  by  Haeckel  "  the  biogenetic 
law,"  will  be  found  especially  pertinent  at  many  stages  in  the 
history  of  science. 

PRIMITIVE  INTERPRETATIONS  OF  NATURE. — As  the  child  thinks 
he  sees  in  almost  everything  some  living  agency,  — because  most  of 
the  things  that  happen  about  him  are  obviously  connected  with 
himself,  or  his  parents,  or  his  nurses,  or  other  children,  or  with 
his  pets,  —  so  man  in  the  childhood  of  the  race  and  in  its  earlier 
development  sees  in  the  wind  some  hidden  being  or  personality 
bending  the  tree,  or  shaking  the  leaves,  or  moaning  or  sighing  in 
the  forest,  or  roaring  angrily  in  thunder.  Only  a  slightly  different 
imagination  is  required  to  see  in  the  sun,  moon,  and  planets  super- 
natural beings  or  gods  travelling  across  the  heavens,  and  by  asso- 
ciation, since  they  seem  to  visit  his  heavens  daily  or  monthly 
or  at  other  regular  intervals,  to  believe  that  they  are  somehow  con- 
cerned with  himself  and  his  welfare  or  destiny.  From  this  primi- 
tive interpretation  to  the  modern  astronomical  knowledge  of  the 
immensity,  the  movements  and  the  paths,  the  temperatures,  and 

1  The  latest  edition  of  Sir  John  Lubbock's  [Lord  Avebury's]  "  Prehistoric  Times  " 
should  also  be  consulted.  Other  easily  accessible  volumes  are  A.  C.  Haddon's 
"  The  Wanderings  of  Peoples  "  (Cambridge  Manuals  of  Science  and  Literature) 
and  J.  L.  Myres'  "The  Dawn  of  History"  (Home  University  Library  Series). 
The  chapters  on  "  Modern  Savages"  in  Lord  Avebury's  "  Prehistoric  Times"  are 
especially  instructive.  Most  important  of  all  is  Professor  H.  F.  Osborn's  recent 
work,  "  Men  of  the  Old  Stone  Age." 


EARLY   CIVILIZATIONS  5 

even  the  chemical  composition,  of  those  enormous  lifeless  masses 
which  we  call  sun,  moon,  and  stars,  has  been  a  long  and  laborious 
journey,  —  how  long  no  one  can  tell.  It  is  still  almost  always 
possible  to  find  tribes  or  peoples  somewhere  on  the  earth  living 
under  one  or  more  of  the  various  conditions  which  the  more 
highly  developed  peoples  have  apparently  passed  through,  and 
there  is  no  great  difficulty  in  finding  primitive  tribes  to-day  holding 
such  childish  interpretations  of  nature  as  we  have  just  described. 
This  circumstance  enables  anthropologists,  ethnologists,  and  his- 
torians to  draw  with  considerable  confidence  the  broader  outlines 
of  the  probable  history  of  the  more  highly  developed  nations, 
such  as  those  of  western  Europe  and  North  America,  —  nations 
in  the  progress  of  which,  since  the  beginning  of  the  nineteenth 
century,  science  has  played  a  notable  part. 

•  The  first  stepping-stones  towards  scientific  knowledge  are 
wonder  and  curiosity,  and  peoples  are  still  to  be  found  so  low  in 
intelligence  as  to  be  almost  destitute  of  curiosity.  As  a  rule, 
however,  most  human  beings,  no  matter  how  primitive,  have 
some  curiosity  concerning,  and  some  sort  of  explanation  for,  the 
commonest  events,  such  as  day  and  night,  life,  death,  sickness, 
health,  sun,  moon,  stars,  winds,  seasons,  and  the  like.  And  one 
of  the  commonest,  simplest,  and  probably  most  natural,  is  that 
already  referred  to  as  the  childish  or  personal  interpretation  of 
nature;  viz.,  that  which  assumes  everything  to  be  in  a  sense 
alive  and  possessed  of  some  sort  of  being,  animation,  or  personality, 
kindred  to  man's  own.  This  primitive  interpretation  has  been 
called  animism.  At  present,  however,  the  term  animalism 
finds  more  favor  among  certain  anthropologists,  apparently  for 
the  reason  that  the  notion  of  mere  diffuse  vitality,  or  general 
"animation,"  is  even  more  primitive,  as  observed  in  certain 
peoples  of  low  development,  than  is  the  idea  of  a  specific  "soul" 
(anima)  differentiated  from  the  body  and  possessing  a  separate 
existence.  For  example,  a  tree  blown  by  the  wind  may  seem  to 
a  man  of  very  low  development  to  be  merely  quivering  with  life, 
and  bending  before  some  more  powerful  but  invisible  influence, 
diffused,  hazy,  unembodied,  and  without  personality  or  name 


6  A   SHORT   HISTORY    OF   SCIENCE 

(animalism}.  Or  it  may  seem  to  be  an  individual  tree,  bent  by 
an  invisible  but  powerful  being  like  a  man  and  perhaps  having  a 
name  such  as  "Boreas"  (the  Greeks'  name  for  the  north  wind). 
In  this  latter  case  we  have  the  assumption  of  personality  and,  by 
analogy  with  man,  of  the  presence  and  influence  of  a  spirit  or 
soul  (animism}. 

PREVALENCE  OF  ANIMISM  IN  ANTIQUITY.  —  Judging  by  the 
opinions  and  beliefs  of  races  which  still  exist  in  very  low 
stages  of  development,  prehistoric  man  when  he  pondered  at 
all,  reasoned  largely  in  the  direction  of  animism.  He  in- 
terpreted himself  and  his  actions  by  his  own  ideas,  will,  feelings, 
and  desires,  and  reasoned  that  other  things  were  actuated  like- 
wise. If,  for  example,  he  killed  an  ox  or  a  man  by  a  blow,  and 
later  an  ox  or  a  man  were  killed  by  lightning,  it  was  reasonable 
to  assume  that  some  invisible  and  manlike  being  had  given  the 
ox  or  man  an  invisible  blow.  The  oldest  records  of  the  human 
race  confirm  this  idea.  The  ancient  Assyrians,  Babylonians,  and 
Egyptians  "animated"  much  of  what  we  today  call  inanimate, 
i.e.  inorganic,  nature ;  and  Greek  and  Hebrew  poetry  are  full  of 
survivals  of  this  view  of  man  and  nature,  which  on  the  higher 
levels  passes  into  personification  and  anthropomorphism.  The 
establishment  of  a  hierarchy  of  the  gods  of  Greece,  such  as  was 
supposed  to  dwell  upon  Mt.  Olympus,  is  merely  a  further  differ- 
entiation of  the  same  kind.  "The  Hellenic  gods  and  goddesses 
are  glorified  men  and  women." 

SOURCES  OF  INFORMATION  CONCERNING  PREHISTORIC  AND 
ANCIENT  TIMES.  —  These  are  of  three  kinds,  tradition,  monuments 
(including  tools,  implements,  pottery,  and  other  objects  which 
have  survived  to  the  present  time,  more  or  less  in  their  original 
form),  and  inscriptions.  Of  these  tradition,  because  readily  sub- 
ject to  perversion,  is  the  least  reliable  and  need  not  be  further 
considered.  It  is  monuments,  such  as  ruins,  tombs,  weapons, 
pottery,  implements,  ornaments,  furniture,  and  the  like,  upon 
which  we  must  chiefly  depend  for  our  knowledge  of  prehistoric 
times,  and  the  evidence  which  has  been  gradually  accumulated 
from  finds  of  this  sort  is  extensive  and  trustworthy  and  corre- 


EARLY   CIVILIZATIONS  7 

spondingly  valuable.  With  the  introduction  of  inscriptions  of  all 
sorts,  including  drawings,  pictures,  hieroglyphics,  and  writings 
of  every  kind,  upon  tablets,  monuments,  walls,  caves,  clay  cylin- 
ders, papyri,  parchments,  and  the  like,  from  about  the  eighth  or 
tenth  century  B.C.,  we  enter  upon  the  historical  period.  From  that 
time  forward  we  have  more  or  less  of  the  raw  material  from  which 
we  may  reconstruct  the  beginnings,  not  only  of  civilization  and 
art,  but  also  of  literature  and  science. 

SOME  ANCIENT  LANDS  AND  PEOPLES.  —  From  the  standpoint 
of  European  history,  and  especially  the  history  of  science,  the  most 
important  peoples  of  antiquity  were  the  Babylonians,  Assyrians, 
Egyptians,  and  Phoenicians.  The  Babylonians  and  Assyrians 
occupied  the  fertile  valley  of  the  Tigris  and  Euphrates ;  the  Egyp- 
tians, that  of  the  Nile ;  and  the  Phoenicians  the  eastern  slopes  of 
the  Mediterranean  basin  (modern  Syria).  The  first  three  peoples 
were  chiefly  agricultural ;  the  last,  chiefly  seafaring,  mercantile,  and 
industrial. 

BABYLONIA  AND  ASSYKIA.  —  These,  lying  almost  side  by  side, 
may  be  considered  together,  although  Babylonia  furnishes  the 
older  and  the  more  important  civilization.  Babylon  and  Nineveh 
were  the  chief  cities  of  the  two  countries,  the  former  in  Mesopo- 
tamia on  the  Euphrates,  the  latter  above  and  to  the  northeast,  and 
much  nearer  the  mountains,  on  the  Tigris. 

In  that  part  of  Asia  which  borders  upon  Africa,  to  the  north  of 
Arabia  and  the  Persian  Gulf,  in  an  almost  tropical  region  at  the  foot 
of  the  Armenian  highlands,  defended  by  mountains  on  the  east  and 
bounded  by  desert  on  the  west,  opens  the  broad  valley  of  the  Tigris 
and  the  Euphrates  rivers  which,  flowing  from  the  same  mountains 
and  in  the  same  direction  and  maintaining  for  a  long  distance  a  parallel 
but  independent  course,  join  at  last  and  fall  together  into  the  Persian 
Gulf.  In  the  month  of  April  these  two  rivers,  swollen  by  the  melted 
snows  in  the  mountains  of  Armenia,  overflow,  sinking  again  to  the 
level  of  their  beds  in  June.  The  country  around  them  therefore  was 
very  similar  to  the  Nile  valley.  A  large  number  of  canals  joined  the 
Tigris  to  the  Euphrates,  and  distributed  the  water  rendered  by  the 
tropical  climate  necessary  for  agriculture. 


8  A   SHORT   HISTORY   OF   SCIENCE 

The  upper  part  of  the  country  inclosed  between  the  two  rivers 
was  properly  called  Mesopotamia,  a  term  used  also  roughly  to  desig- 
nate the  whole.  The  valley  of  the  Upper  Tigris,  or  Upper  Mesopo- 
tamia, was  Assyria,  and  the  lower  part  of  both  valleys  Babylonia.  .  .  . 
In  these  two  fertile  regions  flourished  two  empires,  the  Chaldean- 
Babylonian  and  the  Assyrian. 

The  Chaldeans,  says  a  trustworthy  authority,  appear  to  have  been 
a  branch  of  the  great  Hamite  race  of  Akkad,  which  inhabited  Baby- 
lonia from  the  earliest  times.  With  this  race  originated  the  art  of 
writing,  the  building  of  cities,  the  institution  of  a  religious  system,  and 
the  cultivation  of  all  science,  and  of  astronomy  in  particular.  In  the 
primitive  Akkadian  tongue  were  preserved  all  the  scientific  treatises 
known  to  the  Babylonians.  It  was  in  fact  the  language  of  science  in 
the  East,  as  the  Latin  was  in  Europe  during  the  Middle  Ages.  When 
Semitic  tribes  established  an  empire  in  Assyria  in  the  thirteenth  cen- 
tury B.C.,  they  adopted  the  alphabet  of  the  Akkad,  and  with  certain 
modifications  applied  it  to  their  own  language.  .  .  .  The  mythological, 
astronomical,  and  other  scientific  tablets  found  at  Nineveh,  are  ex- 
clusively in  the  Akkadian  language,  and  are  thus  shown  to  belong  to 
a  priestly  class,  exactly  answering  to  the  Chaldeans  of  profane  history 
and  of  the  Book  of  Daniel.  .  .  . 

From  about  747  B.C.,  the  accession  of  Nabonassar,  the  line  of 
kings  at  Babylon  is  supplied  by  the  well-known  work  of  Ptolemy, 
the  geographer.  .  .  .  Babylon,  according  to  ancient  historians, 
was  surrounded  by  walls  over  three  hundred  feet  in  height  and 
eighty  in  thickness,  and  was  divided  into  two  parts  by  the  river 
Euphrates,  which  flowed  through  it.  Narrow  streets  led  to  the 
river,  on  which  they  opened  by  gates.  Quays  enclosed  the  water, 
and  towards  the  centre  a  bridge  crossed  it,  but  the  bridge  was 
movable  and  was  only  used  during  the  day.  At  night  the  two  sides 
of  the  river  were  completely  separated.  .  .  .  When,  at  the  present 
time,  we  visit  these  formerly  prosperous  countries,  we  can  scarcely 
believe  in  the  universal  fertility  that  so  many  witnesses  have  described. 
The  carelessness  of  the  Turkish  administration  has  allowed  the  irri- 
gation canals  to  be  silted  up,  and  the  inundations  now  form  unhealthy 
swamps  in  the  delta  of  the  Tigris  and  Euphrates.  Mesopotamia  was 
wonderfully  productive  in  wheat  and  barley,  the  enormous  returns 
obtained  by  Bablyonian  farmers  from  their  corn-lands  being  un- 
exampled in  modern  times ;  but  it  possessed  neither  olives,  figs,  nor 


EARLY  CIVILIZATIONS  9 

vines;  millet  and  sesame,  however,  grew  luxuriantly.  Date-palms 
abounded,  and  furnished  a  large  part  of  the  food  of  the  inhabitants. 

The  people  of  Assyria  and  Chaldea  were  as  skilled  in  manual 
handicrafts  as  in  the  cultivation  of  the  earth.  They  wove  cloths  of 
brilliant  colors;  they  also  ornamented  their  garments  with  a  pro- 
fusion of  embroideries,  and  wore  magnificent  tiaras.  Babylonian 
embroidery  was  celebrated  even  in  the  days  of  the  Roman  empire. 
The  manufacture  of  carpets,  one  of  the  chief  luxuries  in  the  East, 
attained  wonderful  perfection  at  Babylon,  as  well  as  the  manufacture 
of  personal  attire.  Their  furniture,  by  its  richness  and  shape,  dif- 
fered completely  from  anything  we  find  in  present  use  amongst  Ori- 
entals ;  the  Assyrians  used  arm-chairs  or  sat  on  stools,  and  dined  as 
we  do  from  tables.  The  tables  and  chairs  were  handsomely  decorated 
and  in  good  taste,  and  it  is  curious  to  note  that  the  same  designs  for 
ornamentation  were  in  use  then  as  we  have  now  —  lions'  claws, 
animals'  heads,  etc. ;  and  even  at  the  present  time  the  ancient  models 
might  be  studied  with  profit  and  copied  with  advantage.  They  were 
skilful  in  working  hard  as  well  as  soft  materials.  The  cylinders  of 
jasper  and  crystal  and  the  bas-reliefs  of  Khorsabad  sculptured  in 
gypsum  or  in  basalt  equally  denote  their  proficiency.  They  were 
acquainted  with  glass  and  with  various  kinds  of  enamel,  and  they 
knew  how  to  bake  clay  for  the  manufacture  of  bricks  or  of  porcelain 
vases.  Moreover,  the  art  of  varnishing  earthenware  and  of  cover- 
ing it  with  paintings  by  means  of  coloured  enamel  was  well  known  at 
Nineveh. 

The  cuneiform  writing  —  so  called  because  it  is  formed  by  pres- 
sure of  the  stylus  on  the  soft  surface  of  the  clay  tablets,  producing 
a  mark  like  a  wedge  or  arrow-head  —  is  a  development  of  hieratic, 
itself  an  improvement  on  the  primitive  hieroglyphic.  The  hieratic 
characters  had  been  scratched  with  the  point  of  the  stylus  on  the 
clay  that  served  the  Mesopotamian  peoples  for  paper.  The  use  of 
the  stylus  in  cuneiform,  gave  a  single  element,  by  the  employment  of 
which  in  various  combinations,  all  the  letters  of  the  alphabet  were 
formed.  When  the  Persians  conquered  Mesopotamia  they  published 
their  decrees,  etc.,  in  the  three  chief  dialects  of  their  subjects  —  the 
Persian,  Median,  and  Assyrian.  Hence  the  trilingual  inscriptions 
which  have  supplied  the  key  to  cuneiform  interpretation.  The  dis- 
covery of  the  interpretation  of  the  famous  inscription  at  Behistun, 
on  the  Persian  frontier,  in  three  languages,  Persian,  Median,  and 


10  A   SHORT   HISTORY   OF   SCIENCE 

Assyrian,  enabled  Sir  Henry  Rawlinson  to  find  the  key  to  the  Assyr- 
ian characters.  .  .  . 

It  is  very  difficult,  in  spite  of  the  numerous  texts  deciphered  by 
modern  savants,  to  form  any  idea  of  Assyrian  literature;  yet  the 
literature  must  have  been  considerable,  for  Layard  found  a  complete 
library  founded  by  King  Asshurbanipal  in  two  of  the  rooms  of  his 
palace  at  Nineveh.  This  library  consisted  of  square  tablets  of  baked 
earth,  with  flat  or  slightly  convex  surface,  on  which  the  cuneiform 
writing  had  been  impressed  while  the  clay  was  soft,  before  baking. 
The  characters  were  very  clearly  and  sharply  defined,  but  many  of 
them  so  minute  as  to  be  read  only  with  the  help  of  a  magnifying  glass. 
These  tablets,  which  are  preserved  at  the  British  Museum,  contain  a 
kind  of  grammatical  encyclopedia  of  the  Assyrio-Babylonian  lan- 
guage, divided  into  treatises ;  and  also  fragments  of  laws,  mythology, 
natural  history,  geography,  etc.  Treatises  on  arithmetic  were  also 
found  in  the  library,  proving  that  mathematical  sciences  were  known, 
with  catalogues  of  observations  of  the  stars  and  planets.  We  have 
already  mentioned  that  astronomy  was  greatly  honored  amongst  the 
Chaldean  priesthood,  who  had  studied  the  course  of  the  moon  with 
so  much  precision  that  they  were  able  to  predict  its  eclipse. 

Science  and  literature  developed,  in  spite  of  a  primitive  writing 
engraved  upon  clay  tablets ;  the  art  of  sculpture  was  already  highly 
refined ;  monuments,  which  without  being  majestic  like  the  Egyptian 
were  imposing  in  their  size  and  splendid  in  their  colours ;  rare  ele- 
gance in  clothing  and  furniture,  denoting  great  wealth,  the  result  of 
active  commerce ;  a  cruel,  even  ferocious  character,  revealed  by  their 
treatment  of  prisoners,  and  indeed  by  all  their  history;  a  learned- 
caste,  devoting  themselves  to  the  sciences  and  also  to  the  unscientific 
methods  of  astrology ;  a  religion  elevated  by  the  primitive  idea  of  a 
supreme  god,  yet  degraded  by  polytheism  and  often  by  gross  de- 
bauchery ;  kings  sufficiently  intelligent  to  construct  splendid  palaces 
and  immense  cities,  and  yet  inflated  with  pride  and  glorying  in  the 
most  stupid  cruelty  —  such  is  the  picture  opened  to  us  by  the  records 
of  Assyrian  and  Babylonian  history.  When  we  observe  on  the 
Assyrian  bas-reliefs  all  the  industries  and  all  the  arts,  we  are  inclined 
to  acknowledge  that  they  were  superior  to  the  nations  that  surrounded 
them,  and  we  understand  how  the  Greeks  drew  inspiration  from 
Assyrian  work  as  well  as  from  Egyptian.  —  Verschoyle.  History  of 
Civilization. 


EARLY   CIVILIZATIONS  11 

If,  in  a  final  summing  up,  the  question  be  asked,  What  was  the 
legacy  which  Babylonia  and  Assyria  left  to  the  world  after  an  exist- 
ence of  more  than  three  millenniums,  the  answer  would  be,  that  through 
the  spread  of  dominion  the  culture  of  the  Euphrates  Valley  made  its 
way  throughout  the  greater  part  of  the  ancient  world,  leaving  its  im- 
press in  military  organization,  in  the  government  of  people,  in  com- 
mercial usages,  in  the  spread  of  certain  popular  rites  such  as  the 
various  forms  of  divination,  in  medical  practices  and  in  observation 
of  the  movements  of  heavenly  bodies — albeit  that  medicine  continued 
to  be  dependent  upon  the  belief  in  demons  as  the  source  of  physical 
ills,  and  astronomy  remained  in  the  service  of  astrology  —  and  lastly 
in  a  certain  attitude  towards  life  which  it  is  difficult  to  define  in 
words,  but  of  which  it  may  be  said  that,  while  it  lays  an  undue  em- 
phasis on  might,  is  yet  not  without  an  appreciation  of  the  deeper 
yearnings  of  humanity  for  the  ultimate  triumph  of  what  is  right. 
—  Morris  Jastrow,  Jr.  The  Civilization  of  Babylonia  and  Assyria. 

EGYPT.  —  Another  highly  important  ancient  civilization  whose 
beginnings  are  lost  for  us  in  the  darkness  of  prehistoric  times  is 
that  which  flourished  in  the  valley  of  the  Nile. 

Near  the  point  where  Africa  approaches  Asia  lies  a  narrow  valley, 
walled  in  by  two  ranges  of  mountains,  enclosed  on  the  farther  side  by 
two  deserts,  and  fertilized  by  the  periodical  inundations  of  a  mighty 
river.  This  long  and  narrow  strip  of  verdure,  surrounded  by  moun- 
tains and  menaced  by  the  desert  sands,  is  Egypt.  ...  A  few  years 
ago,  the  beginnings  of  Egyptian  history,  and  even  the  source  of  the 
great  river  that  fertilizes  the  land  of  Egypt,  were  hidden  in  mystery. 
The  sources  of  the  Nile  have  been  at  last  discovered,  and  archaeo- 
logists have  now  retraced  the  commencement  of  a  history  which  is 
practically  the  commencement  of  all  authentic  history.  To  Speke 
and  Grant  in  1862,  and  to  Baker  in  1864,  we  owe  the  knowledge  of 
the  lakes  Victoria  Nyanza  and  Albert  Nyanza,  whence  come  the 
abundant  waters,  that  swollen  by  the  equatorial  rains,  at  fixed  in- 
tervals overflow  and  fertilize  with  their  mud  the  soil  that  borders  their 
bed,  and  refresh  a  land  which  lies  beneath  a  sky  where  a  rain-cloud  is 
seldom  seen.  We  know,  too,  how  the  abundant  harvests  that  regu- 
larly result  from  the  inundations  of  the  Nile,  returning  ample  food  to 
moderate  labour,  promoted  the  development  of  the  Egyptian  nation ; 


12  A   SHORT   HISTORY   OF   SCIENCE 

how  the  Nile  itself  supplied  to  them  a  highway  for  communication, 
rendered  doubly  useful  by  the  north  winds  that  blow  up  stream 
more  than  eight  months  of  the  year,  carrying  the  traffic  up  into 
the  interior  while  the  current  carries  it  down;  how  the  Arabian 
desert  on  the  east  and  the  Libyan  on  the  west  secured  to  them 
comparative  immunity  from  invasion  and  opportunity  for  internal 
progress.  .  .  . 

One  of  the  prizes  of  Napoleon's  expedition,  a  black  basalt  stone, 
disinterred  at  Rosetta  in  1798,  and  now  in  the  British  Museum,  bore 
three  parallel  and  horizontal  inscriptions,  all  quite  distinct.  One  was 
in  hieroglyphics,  the  second  in  the  characters  called  demotic  or  popu- 
lar, the  third  in  Greek.  Although  a  great  many  scientific  men  ex- 
hausted their  skill  upon  this  trilingual  inscription,  which  was  a  triple 
inscription  of  the  same  text,  no  one  could  make  the  Greek  characters 
exactly  apply  to  the  hieroglyphic  signs.  Champollion  was  the  first 
to  obtain  any  success,  as  early  as  1812,  but  further  progress  was  largely 
aided  by  the  labors  of  Thomas  Young  [a  name  associated  in  the 
history  of  science  with  those  of  Fresnel  and  Helmholtz].  .  .  . 

Protected  from  invasion  by  the  same  deserts  that  isolated  them, 
the  people  who  came  from  Asia  and  settled  in  the  Nile  valley  applied 
themselves  to  the  regulation  of  the  periodical  inundations,  and  to  the 
distribution  of  the  water.  They  built  towns  on  the  hillocks,  in  order 
that  the  water  should  not  reach  them;  and  afterwards,  with  the 
stones  that  the  two  mountain  ranges  of  Libya  and  Arabia  contain  in 
abundance,  and  by  the  means  of  transit  afforded  by  the  Nile,  they 
erected  monuments  that  have  defied  the  course  of  the  centuries.  .  .  . 

The  paintings  in  the  tombs  also  show  us  men  at  work  upon  all 
the  arts  and  all  the  handicrafts.  '  We  see  there  the  workers  in  stone 
and  in  wood,  the  painters  of  sculpture  and  of  architecture,  of  furni- 
ture and  carpenters'  work;  the  quarrymen  hewing  blocks  of  stone; 
all  the  operations  of  the  potter's  art;  workmen  kneading  the  earth 
with  their  feet,  or  with  their  hands ;  men  at  work  making  stocks,  oars 
and  sculls;  curriers,  leather-dyers,  and  shoe-makers,  spinners,  cloth- 
weavers  with  various  shaped  looms,  glass-makers;  goldsmiths,  jew- 
ellers, and  blacksmiths.'  Among  the  antiquities  still  in  a  state  of 
good  preservation  there  is  much  pottery,  including  vessels  of  simple 
earthenware  and  enamelled  faience,  enamelled  and  sculptured  terra- 
cotta, glass,  often  resembling  Venetian,  metal  work  and  jewellery, 
and  linen  cloth  as  fine  as  Indian  muslin.  —  Verschoyle. 


EARLY  CIVILIZATIONS  13 

PHOENICIA.  —  Two  other  civilizations  of  importance,  the 
Phoenician  and  the  Hebrew,  existed  in  antiquity  between  the 
Mediterranean  Sea  and  the  great  Arabian  desert,  in  what  are 
to-day  called  Syria  and  Palestine. 

By  the  side  of  the  Hebrew  nation,  which  owed  its  grandeur  to 
its  moral  and  religious  development,  dwelt  the  Phoenicians,  a  people 
who  owed  their  fame  to  their  maritime  and  commercial  enterprise. 
They  occupied  a  narrow  strip  of  land  between  Lebanon  and  the 
Mediterranean,  Phoenicia  proper  being  but  28  miles  long  by  one  to 
five  miles  broad,  and  the  territory  of  the  Phoenicians  being,  at  the 
utmost,  no  more  than  120  miles  long  by  20  wide.  .  .  .  The  forests 
which  clothed  the  chain  of  Lebanon  supplied  the  Phoenicians  with 
timber  for  their  ships,  and  they  soon  made  the  Mediterranean  a  high 
road  for  their  navy.  Enclosed  by  mountains  in  a  country  that 
prevented  their  acquiring  any  inland  empire,  they  became  a  maritime 
power,  the  first  in  the  ancient  world  in  order  of  importance  as  in 
order  of  time.  Egyptian  documents  mention  the  Phoenician  towns 
of  Gebal,  Beryta,  Sidon,  Sarepta,  etc.,  as  early  as  sixteen  or  seven- 
teen centuries  before  the  Christian  era.  The  Phoenicians  served  as 
middlemen  to  the  great  civilizations  of  the  Nile  and  the  Euphrates, 
their  vessels  easily  coasting  along  to  the  mouth  of  the  Nile,  and  their 
caravans  having  but  a  short  journey  to  reach  the  point  where  the  mid- 
dle Euphrates  almost  touches  Upper  Syria,  whence  the  current  would 
carry  them  down  to  the  quays  of  Babylon.  ...  To  the  westward 
the  Phoenicians  sailed  beyond  the  Mediterranean  and  ventured  upon 
the  Atlantic  Ocean.  They  coasted  the  western  side  of  Africa,  and 
early  accounts  record  their  discoveries  of  wonderful  islands  of  mar- 
vellous fertility  and  charming  climate,  the  '  Fortunate  Isles/  — 
probably  Madeira  and  the  Canaries.  They  also  sailed  along  the 
coasts  of  Spain  and  Western  France  and  reached  Northern  Europe. 
Gades  (Cadiz)  was  the  starting  point  for  these  long  and  dangerous 
voyages,  which  extended  as  far  as  Great  Britain,  where  a  considerable 
trade  in  tin  was  carried  on.  ...  The  Phoenicians  were  the  great 
mining  people  of  the  ancient  world.  Gold,  silver,  iron,  tin,  lead,  cop- 
per, and  cinnabar  were  obtained  from  Spain,  still  the  chief  metallif- 
erous country  of  Southern  Europe.  The  details  given  by  Diodorus 
concerning  the  Spanish  mines  are  very  circumstantial.  'The  cop- 
per, gold,  and  silver  mines  are  wonderfully  productive/  and  'those 


14  A   SHORT   HISTORY   OF   SCIENCE 

who  work  the  copper  mines  draw  from  the  rough  ore  one  quarter  of 
the  weight  in  pure  metal/  .  .  .  The  Phoenicians  not  only  brought 
the  mineral  wealth  of  Spain  to  the  Eastern  world,  but  they  had  also 
a  great  trade  in  wheat,  wine,  oil,  fruits  of  all  kinds,  and  fine  wool. 
They  provided  Asia  with  the  products  of  Spain  and  Gaul,  Sicily  and 
Africa  with  the  products  of  Asia.  But  this  maritime  commerce  could 
only  be  supplied  by  an  inland  trade,  which  served  to  connect  the 
countries  that  were  a  long  distance  from  the  sea.  Phoenicia  found 
itself  one  of  the  ports  of  Asia,  the  merchandise  of  distant  countries 
was  brought  to  it,  and  from  it  was  exported  all  the  produce  of  the 
Asian  continent.  The  caravans  supplemented  the  fleets,  and  the 
fleets  distributed  the  burdens  of  the  caravans.  The  land  trade  was 
chiefly  in  three  directions  —  to  the  south  it  followed  the  route  to 
Arabia  and  India ;  to  the  east,  that  to  Assyria  and  Babylon ;  to  the 
north,  that  to  Armenia  and  the  Caucasus. 

The  Phoenicians  were  not  only  the  great  maritime,  the  great 
commercial,  and  the  great  mining  power  of  antiquity,  they  were  also 
one  of  the  chief  manufacturing  powers.  Like  the  Egyptians  and 
Assyrians,  they  were  skilful  potters,  and  they  discovered  the  art  of 
making  glass.  'It  is  said/  writes  Pliny  the  elder,  'that  some  Phoeni- 
cian merchants,  having  landed  on  the  shores  of  the  river  Belus,  were 
preparing  their  meal,  and  not  finding  suitable  stones  for  raising  their 
saucepans,  they  used  lumps  of  natron,  contained  in  their  cargo,  for 
the  purpose.  When  the  natron  was  exposed  to  the  action  of  the  fire, 
it  melted  into  the  sand  lying  on  the  banks  of  the  river,  and  they  saw 
transparent  streams  of  some  unknown  liquid  trickling  over  the  ground ; 
this  was  the  origin  of  glass/  No  matter  how  it  may  have  originated, 
there  is  no  doubt  that  the  Phoenicians  manufactured  glass  on  a  large 
scale,  and  then*  glass-work  became  celebrated  all  over  the  world. 
Dyeing  works,  however,  take  the  first  rank  among  Phoenician  indus- 
tries, and  Tyrian  purple  was  one  of  the  chief  objects  of  luxury  among 
the  ancients.  The  word  '  purple '  was  not  used  only  for  a  single  colour, 
but  for  a  particular  kind  of  dye,  for  which  animal  colours  obtained 
from  the  juice  of  certain  shellfish  were  used.  The  dyeing  works  could 
not  be  carried  on  without  cloths,  for  the  Phoenicians  dyed  woollen 
materials  chiefly  with  their  famous  purple.  The  wool  came  from 
Damascus,  and  the  greater  part  of  their  export  of  woollen  stuffs  was 
doubtless  of  their  own  manufacture.  Sidon  was  the  first  town  that 
became  noted  for  these  fabrics.  Homer  often  mentions  tunics  from 


EARLY   CIVILIZATIONS  15 

that  town,  but  afterwards  they  were  manufactured  all  over  Phoenicia, 
and  particularly  at  Tyre.  Among  the  products  of  Phoenician  in- 
dustry we  must  also  mention  the  numerous  ornaments  and  the  articles 
whose  value  depends  largely  on  their  workmanship.  The  trade  of 
barter  which  they  had  so  long  maintained  with  barbaric  races,  amongst 
whom  these  objects  always  find  an  appreciative  market,  had  incited 
the  Phoenicians  to  apply  themselves  to  these  industries.  Chains  of 
artistically  worked  gold  were  worn  by  Phoenician  navigators  in  Homer's 
time,  and  Ezekiel  mentions  their  curious  work  in  ivory,  which  they 
procured  through  Assyria  from  India,  and  from  Ethiopia.  Accident 
has  preserved  the  names  of  only  a  small  number  of  the  articles  pro- 
duced by  the  Phoenicians,  but  the  existence  of  these  among  a  rich 
and  luxurious  people  implies  the  existence  of  others. 

The  Phoenician  religion  was  a  worship  of  personified  forces  of 
nature,  especially  of  the  male  and  female  principles  of  reproduction. 
It  was  in  a  popular  and  simple  form  a  worship  of  the  sun,  the  moon, 
and  the  five  planets,  regarded  as  intelligent  powers  actively  affecting 
human  life.  .  .  .  And  the  Phoenician  religion  not  only  consecrated 
licentiousness,  it  also  sanctioned  cruelty.  Living  children  were 
offered  as  burnt  sacrifices  to  Baal  as  well  as  to  Moloch.  One  can 
scarcely  understand  how  human  sacrifices  could  have  been  endured 
by  an  intelligent  people;  but  this  abominable  ritual  was  in  force  in 
all  the  colonies,  and  especially  at  Carthage,  where  during  the  siege  of 
the  city  by  Agathocles,  about  307  B.C.,  two  hundred  boys  of  the  best 
families  were  offered  as  burnt  sacrifices  to  the  planet  Saturn. 

Though  we  have  but  few  fragments  of  Phoenician  antiquities  and 
literature,  we  at  least  know  their  system  of  writing.  It  is  now  proved 
that  the  Phoenicians  did  not  invent  writing ;  they  merely  communi- 
cated letters  to  the  Greeks.  .  .  .  The  Greeks  adopted  the  Phoenician 
characters  with  only  a  few  modifications;  the  Latin  races  used  the 
same  letters  designed  more  simply;  they  had  received  them  at  a 
very  remote  date,  for  the  Latin  tongue  was  a  sister  not  a  daughter  of 
the  Greek.  The  French,  Spanish,  and  Italian  languages  are  all 
derived  from  the  Latin  and  use  the  same  characters,  while  even  the 
Teutonic  languages,  like  English  and  German,  have  adopted  this 
alphabet.  The  Phoenicians  must,  on  this  ground  alone,  take  high 
rank  in  the  history  of  civilization.  .  .  . 

The  Phoenicians  were  not  only  the  pioneers  of  industry,  but  by 
their  commerce  they  brought  together  the  peoples  of  the  three  con- 


16  A   SHORT   HISTORY   OF   SCIENCE 

tinents  of  the  Old  World.  The  first  carriers  by  sea,  acting  as  inter- 
mediate agents  between  the  different  nations,  they  exchanged  ideas 
as  well  as  merchandise;  their  exploration  of  different  countries  led 
to  the  discovery  of  new  riches;  they  endowed  the  West  with  the 
products  of  the  East,  and  the  East  with  the  products  of  the  West. 
They  proved  to  the  world  that  cities  can  attain  a  high  degree  of  pros- 
perity by  labour,  activity,  and  economy,  and  they  remain  examples  of 
the  highest  development  of  purely  commercial  qualities.  —  Verschoyle. 

THE  HEBREWS.  —  South  of  Phoenicia  and  lying  between  the 
Arabian  Desert  and  the  Mediterranean  was  Palestine :  — 

The  whole  literature  of  the  Hebrews  is  included  in  the  collection 
of  prose  and  poetry  which  we  call  the  Bible,  or,  more  accurately,  the 
Old  Testament.  The  simplicity  of  its  narratives,  the  enthusiasm  of 
its  hymns,  the  joyful  or  plaintive  melody  of  the  psalms,  the  fiery 
eloquence  of  the  prophets,  place  the  Bible,  independently  of  its  re- 
ligious and  historical  importance,  high  among  the  great  literary 
monuments  of  antiquity.  Their  literature  is  a  proof  that  the  poetic 
imagination  was  fully  developed  amongst  the  Hebrews,  and  that  the 
people  were  deeply  thoughtful  as  well  as  passionately  religious.  .  .  . 
The  Hebrews  were  not  an  artistic  or  an  industrial  people ;  but  they 
possessed  an  indisputable  superiority  to  all  other  nations  of  antiquity 
in  their  purely  spiritual  religion,  and  in  their  appreciation  of  the 
supreme  importance  of  morals  as  the  proper  expression  of  religion. 
Religion  was  their  rule  of  life,  the  maker  of  their  laws,  the  pervading 
spirit  of  the  whole  community,  as  in  no  other  nation  before  or  since. 

—  Verschoyle. 

THE  EMERGENCE  OF  EUROPEAN  CIVILIZATION.  —  Until  very 
recently  little  was  known  of  European  events  before  the  writings 
of  Herodotus  (484-425  B.C.).  Within  the  last  half  century,  how- 
ever, and  largely  as  a  result  of  the  labors  of  the  archaeologists 
Schliemann  and  Evans,  the  existence  of  a  wonderfully  rich  and 
complete  prehistoric  civilization  has  been  revealed  on  the  shores 
and  islands  of  and  near  the  Greek  Peninsula. 

The  recent  discoveries  in  Crete  have  added  a  new  horizon  to 
European  civilization.  A  new  standpoint  has  been  at  the  same  time 


EARLY   CIVILIZATIONS  17 

obtained  for  surveying  not  only  the  ancient  classical  world  of  Greece 
and  Rome,  but  also  the  modern  world  in  which  we  live.  —  Sir 
Arthur  Evans. 

AEGEAN  CIVILIZATION  IN  THE  BRONZE  AGE.  —  The  newer 
European  civilization  had  also  its  prehistoric  times,  and  the 
investigations  and  especially  the  excavations  of  the  last  half 
century  have  revealed  such  treasures  as  the  site  of  Homeric  Troy, 
the  palace  and  tomb  of  Agamemnon,  and  the  cities  of  Minos  and 
others  of  the  sea  kings  of  Crete.  It  is  now  known  that  the  Trojan 
War  was  fought  about  Hissarlik  on  the  eastern  shore  of  the  Dar- 
danelles; that  Agamemnon's  palace  was  at  Mycenae  in  Greek 
Argolis;  and  that  Minos  had  his  home  and  his  naval  base  of 
Mediterranean  sea  power  on  the  island  of  Crete.  In  Mycenae 
and  in  Crete  the  arts  were  highly  developed.  Painting,  sculpture, 
and  pottery,  tools,  weapons,  implements  of  various  kinds,  with 
systems  of  water  supply  and  drainage,  testify  to  the  remarkable 
degree  of  civilization  attained  in  the  later  Bronze  Age,  although 
this  has  left  behind  it  no  written  records  and  was  formerly  known 
to  us  only  through  the  poems  of  Homer. 

Even  to  classical  students  twenty,  nay,  ten  years  ago,  Crete  was 
scarcely  more  than  a  land  of  legendary  heroes  and  rationalized  myths. 
It  is  true  that  the  first  reported  aeronautical  display  was  made  by  a 
youth  of  Cretan  parentage,  but  in  the  absence  of  authenticated  records 
of  the  time  and  circumstances  of  his  flight,  scholars  were  sceptical  of 
his  performance.  And  yet  within  less  than  ten  short  years  we  are 
faced  by  a  revolution  hardly  more  credible  than  this  story;  we  are 
asked  by  archaeologists  to  carry  ourselves  back  from  A.D.  1910  to 
1910  B.C.,  and  witness  a  highly  artistic  people  with  palaces  and  treas- 
ures and  letters,  of  whose  existence  we  had  not  dreamed.  .  .  . 

The  theme  is  a  fresh  one,  because  nothing  was  known  of  the  subject 
before  1900 ;  it  is  important,  because  the  Golden  Age  of  Crete  was  the 
forerunner  of  the  Golden  Age  of  Greece,  and  hence  of  all  our  western 
culture.  The  connection  between  Minoan  [Cretan]  and  Hellenic 
civilization  is  vital,  and  not  one  of  locality  alone,  as  is  the  tie  between 
the  prehistoric  and  the  historic  of  America,  but  one  of  relationship. 
Egypt  may  have  been  foster-mother  to  classical  Greece,  but  the 
mother,  never  forgotten  by  her  child,  was  Crete.  .  .  . 
c 


18  A   SHORT   HISTORY   OF   SCIENCE 

Members  of  three  foreign  nations  have  worked  in  friendly  rivalry 
to  learn  the  buried  history  of  Crete  .  .  .  and  Cretan  soil  may  be 
said  to  have  been  found  to  teem  with  pre-Hellenic  antiquities.  The 
hopes  of  archaeologists  have  been  abundantly  justified.  We  have 
followed  them  and  arrived  at  the  home  of  the  first  European  civili- 
zation. —  Hawes.  Crete,  the  Forerunner  of  Greece. 

Even  at  this  exceedingly  early  stage  of  human  progress,  the  va- 
rious branches  of  industry  had  become  fairly  separated  and  specialized, 
more  so,  perhaps,  than  in  the  Homeric  period,  and  a  considerable 
variety  of  tools  was  employed  in  the  various  crafts.  The  carpenter 
was  evidently  a  highly  skilled  craftsman,  and  the  tools  which  have 
survived  show  the  variety  of  work  which  he  undertook.  At  Knossos 
a  carefully  hewn  tomb  held,  along  with  the  body  of  the  dead  artificer, 
specimens  of  the  tools  of  his  trade  —  a  bronze  saw,  adze,  and  chisel. 
'  A  whole  carpenter's  kit  lay  concealed  in  a  cranny  of  a  Gournia  house 
left  behind  in  the  owner's  hurried  flight  when  the  town  was  attacked 
and  burned.  He  used  saws  long  and  short,  heavy  chisels  for  stone 
and  light  for  wood,  awls,  nails,  files,  and  axes  much  battered  by  use ; 
and  what  is  very  important  to  note,  they  resemble  in  shape  the  tools 
of  to-day  so  closely  that  they  furnish  one  of  the  strongest  links 
between  the  first  great  civilization  of  Europe  and  our  own.'  Such 
tools  were,  of  course,  of  bronze.  Probably  the  chief  industry  of  the 
island  was  the  manufacture  and  export  of  olive  oil.  The  palace  at 
Knossos  has  its  Room  of  the  Olive  Press,  and  its  conduit  for  convey- 
ing the  product  of  the  press  to  the  place  where  it  was  to  be  stored  for 
use ;  and  probably  many  of  the  great  jars  now  in  the  magazines  were 
used  for  the  storage  of  this  indispensable  article.  —  Baikie.  Sea 
Kings  of  Crete. 

THE  IRON  AGE.  THE  GREEKS  OR  HELLENES.  —  Soon  after  the 
arrival  of  the  Iron  Age,  and  probably  not  far  from  1200-1000  B.C., 
a  new  people  became  prominent  on  the  shores  of  the  ^Egean. 
These  were  the  Greeks  or,  as  they  called  themselves,  Hellenes,  — 
inhabitants  of  Greece  or  Hellas.  Their  precise  origin  is  unknown, 
but  they  were  undoubtedly  of  Indo-European  stock  and  probably 
came,  in  part  at  least,  from  the  north.  It  has  been  conjectured 
that  their  conquest  of  the  existing  inhabitants  was  facilitated  by, 
if  not  due  to,  their  possession  of  weapons  of  iron.  Of  the  earlier 


EARLY   CIVILIZATIONS  19 

part  of  this  new  period  (1200-800  B.C.)  we  have  only  the  legendary 
accounts  of  the  Homeric  and  Hesiodic  poems,  which  are  now  gen- 
erally believed  to  be  based  upon,  if  not  actually  descriptive  of, 
episodes  of  this  age. 

The  Hellenes  soon  supplanted  the  Phoenicians  as  traders  in  the 
southern  ^Egean ;  and  "  if  we  now  leave  the  monuments  of  the 
Egyptian  temple  or  the  Assyrian  palace  and  turn  to  the  pages  of 
the  Iliad  and  the  Odyssey  ...  at  once  we  are  in  the  open  air, 
and  in  the  sunshine  of  a  natural  life.  The  human  faculties  have 
free  play  in  word  and  deed.  .  .  From  the  first  the  Greek  is  re- 
solved to  confront  the  facts  of  life."  —  Jebb. 

REFERENCES  FOR  READING 

OSBORN,  H.  F.    Men  of  the  Old  Stone  Age. 

LUBBOCK,  SIR  JOHN  (LORD  AVEBURY).    Prehistoric  Times  (7th  Edition). 

MYRES,  J.  L.     The  Dawn  of  History. 

TYLOR,  E.  B.    Anthropology  and  Primitive  Culture. 

H  ADDON,  A.  C .    History  of  A  nthropology. 

JASTROW,  MORRIS,  Jr.     The  Civilization  of  Babylonia  and  Assyria. 

HAWES,  C.  H.  AND  H.     Crete,  the  Forerunner  of  Greece. 

SPEARING,  H.  G.     The  Childhood  of  Art. 


CHAPTER  II 

EARLY  MATHEMATICAL  SCIENCE  IN  BABYLONIA  AND 

EGYPT 

In  most  sciences  one  generation  tears  down  what  another  has  built 
and  what  one  has  established  another  destroys.  In  Mathematics  alone 
each  generation  builds  a  new  story  to  the  old  structure.  —  Hankel 

A  HISTORY  of  science  may  be  based  on  some  more  or  less  definite 
logical  system  of  definitions  and  classifications.  As  a  matter  of 
historical  evolution,  however,  such  systems  and  such  points  of 
view  belong  to  relatively  recent  and  mature  periods.  Science 
has  grown  without  very  much  self-consciousness  as  to  how  it  is 
itself  defined,  or  any  great  concern  as  to  the  distinction  between 
pure  and  applied  science,  or  as  to  the  boundaries  between  the 
different  sciences.  Mathematics,  for  example,  has  had  its  roots  in 
the  human  need  of  exact  statement  as  to  both  number  and  form  in 
all  sorts  of  affairs,  and  on  the  other  hand  in  the  analytical  faculties 
of  the  human  mind,  which  have  shaped  the  development  of  the  pure 
science  and  given  it  in  course  of  time  its  deductive  stamp. 

The  origin  of  a  science  can  seldom  be  precisely  determined,  and 
the  more  ancient  the  science  the  more  difficult  is  the  attainment 
of  such  precision.  The  periods  at  which  primitive  men  of  different 
races  began  to  have  conscious  appreciation  of  the  phenomena  of 
nature,  of  number,  magnitude,  and  geometric  form,  can  never  be 
known,  nor  the  time  at  which  their  elementary  notions  began  to 
be  so  classified  and  associated  as  to  deserve  the  name  of  science. 
Very  early  in  any  civilization,  however,  mathematics  must  ob- 
viously have  taken  its  rise  in  simple  processes  of  counting  and 
adding,  of  time  measurement  in  primitive  astronomy,  of  the  geom- 
etry and  arithmetic  involved  in  land  measurement  and  in  archi- 
tectural design  and  construction.  We  can  safely  sketch  certain 
rough  outlines  of  the  prehistoric  picture,  and  we  can  to  some  extent 

20 


BABYLONU  AND  EGYPT  21 

verify  these,  on  the  one  hand,  by  archseological  evidence,  on  the 
other,  by  present-day  observations  of  backward  races  —  still  in 
their  prehistoric  stage. 

PRIMITIVE  ASTRONOMICAL  NOTIONS.  —  On  the  astronomical  side 
the  most  obvious  fact  is  the  division  of  time  into  periods  of  light  and 
darkness  by  the  apparent  revolution  of  the  sun  about  the  earth. 
With  closer  attention  it  must  soon  have  been  observed  that  the  rela- 
tive length  of  day  and  night  gradually  changes,  and  that  this 
change  is  attended  by  a  wide  range  of  remarkable  phenomena.  At 
the  time  of  shortest  days,  vegetable  and  animal  life  (in  the  north 
temperate  zone)  is  checked  by  severe  cold.  With  the  gradually 
lengthening  days,  however,  snow  and  ice  sooner  or  later  disap- 
pear, vegetation  is  revived,  birds  return  from  the  warmer  south, 
all  nature  is  quickened.  In  the  symbolism  of  the  beautiful  old 
myth,  the  sleeping  princess,  our  earth,  is  aroused  by  the  kiss  of  the 
sun-prince.  The  longest  days  and  those  which  succeed  them 
are  a  period  of  excessive  heat  and  of  luxuriant  vegetation,  followed 
by  harvests  as  the  days  shorten,  towards  the  completion  of  the 
great  annual  cycle.  In  time,  closer  observers,  noting  the  stars,  dis- 
covered that  corresponding  with  this  great  periodic  change  are 
gradual  variations  in  the  starry  hemisphere  visible  at  night,  that 
in  other  words  the  sun's  place  among  the  stars  is  progressively 
changing,  that  it  is  in  fact  describing  a  path  completed  in  a  large 
number  of  days,  which  after  repeated  counting  is  found  to  be  365. 
It  is  also  found  that  the  midday  height  of  the  sun  above  the 
southern  horizon  shares  in  the  annual  cycle.  The  determination 
of  the  number  of  days  in  the  year  is  a  matter  of  very  gradual  ap- 
proximation, possible  only  to  men  who  have  already  attained 
some  command  of  numbers  and  the  habit  of  preserving  records 
extending  over  a  long  series  of  years.  For  there  is  no  well-marked 
beginning  of  the  year  as  of  the  day.  An  erroneous  determination 
of  the  number  of  days  becomes  apparent  only  after  a  number  of 
years,  increasing  with  the  accuracy  of  the  original  approximation. 
If,  for  example,  the  year  is  assumed  to  be  exactly  365  days,  that 
is,  about  six  hours  too  short,  the  festivals  and  other  dates  will  slip 
back  about  24  days  in  a  century,  and  thus  lose  their  original  cor- 


22  A   SHORT  HISTORY  OF  SCIENCE 

respondence  with  climatic  conditions.  A  revision  of  the  calendar 
will  become  necessary. 

Still  another  natural  period  is  introduced  by  the  motion  of  the 
moon,  which  seems  like  the  sun  jto  have  a  daily  motion  about 
the  earth,  and  also  to  describe  a  jclosed  path  among  the  stars  in  a 
period  of  about  29  days.  Unlikk  the  sun,  however,  the  moon  has 
during  this  period  a  remarkable  change  of  apparent  shape  and 
luminosity  from  "  new  "  to  "  full "  and  back  again.  The  study  of  the 
day,  the  year,  the  month,  thus  naturally  determined  by  the  great 
heavenly  bodies  has  led  to  the  development  of  the  calendar  with 
greater  and  greater  accuracy,  the  most  recent  rectification  of 
the  length  of  the  year  dating  only  (in  England)  from  1752.  The 
difficulty  of  expressing  the  precise  length  of  the  month  and  the 
year  in  days,  causing  the  imperfection  of  early  calendars,  has,  on 
the  other  hand,  reacted  to  the  advantage  of  mathematical  as- 
tronomy by  demanding  the  greatest  possible  precision  both  of 
observation  and  of  the  computation  based  upon  it. 

THE  PLANETS.  —  Another  celestial  phenomenon,  though  less  ob- 
vious than  the  foregoing,  must  have  found  wide  recognition  in  pre- 
historic times.  The  stars  vary  widely  in  grouping  and  individual 
brilliancy,  but  in  general  their  relative  positions  are  sensibly 
constant.  To  this  constancy,  however,  five  exceptions  are  easily 
discovered  in  the  wandering  motion  of  the  planets  Mercury,  Venus, 
Mars,  Jupiter,  and  Saturn,  which  like  sun  and  moon  have  their 
several  paths  among  the  stars  but  with  seemingly  irregular  mo- 
tions. Corresponding  to  these  seven  bodies  there  was  set  up  by 
prehistoric  people  an  arbitrary  division  of  time  into  weeks  of  seven 
days,  "the  most  ancient  monument  of  astronomical  knowledge." 
The  correspondence  with  the  planets  is  still  preserved  in  the 
names  of  the  days  of  the  week  in  several  modern  languages.1  The 

FRENCH  ITALIAN 

1  Sunday  dimanche  domenica  (Sun) 

Monday  lundi  lunedi  (Moon) 

Tuesday  mardi  martedi  (Mars) 

Wednesday  mercredi  mercoledi  (Mercury) 

Thursday  jeudi  giovedi  (Jupiter) 

Friday  vendredi  venerdi  (Venus) 

Saturday  samedi  sabato  (Saturn) 


BABYLONIA  AND  EGYPT  23 

further  division  of  time  into  hours,  minutes,  and  seconds  has 
followed  more  arbitrarily,  and  in  connection  with  the  develop- 
ment of  progressively  improved  methods  of  time  measurement. 

ASTROLOGY  AND  COSMOLOGY.  —  Side  by  side  with  the  develop- 
ment of  elementary  astronomy  on  its  observational  and  mathemati- 
cal sides  were  evolved  in  intimate  connection  with  it,  but  sometimes 
in  extraordinary  imaginative  forms,  astrology  and  cosmology, 
dealing  respectively  with  the  supposed  influence  of  the  heavenly 
bodies  on  human  affairs,  and  with  the  structure  and  organization 
of  the  world.  Both  these  pseudo-sciences  were  inextricably 
blended,  under  priestly  and  literary  influences,  with  a  bewildering 
mass  of  superstition  and  mythology,  legend  and  invention.  In 
their  earlier  stages,  both  doubtless  contributed  powerfully  to 
interest  and  progress  in  real  science.  Ultimately  both  have  had 
to  be  torn  away,  as  the  scaffolding  from  a  cathedral,  in  the  never 
ending  process  of  releasing  truth  from  error. 

PRIMITIVE  COUNTING.  —  On  the  arithmetical  side  the  present 
counting  processes  of  primitive  peoples  have  particular  interest. 
The  distinction  between  one  and  two  similar  objects,  and  that 
between  two  and  three  or  more,  belong  to  a  relatively  early  stage 
of  development,  but  tribes  are  known  to-day  in  which  the  entire 
number  scale  is  one,  two,  many  (i.e.  more  than  two).  The  pro- 
cess of  counting  is  naturally  facilitated  by  the  use  of  fingers  and 
toes  as  counters,  their  number  10  being  the  well-known  anatomi- 
cal basis  for  our  denary  or  decimal  number  system.  This  may  be 
illustrated  by  the  following  passages  from  E.  B.  Tylor's  Primitive 
Culture :  — 

Father  Gilij,  describing  the  arithmetic  of  the  Tamanacs  on  the 
Orinoco,  gives  their  numerals  up  to  4;  when  they  come  to  5,  they 
express  it  by  the  word  amgnaitone,  which  being  translated  means  '  a 
whole  hand ' ;  6  is  expressed  by  a  term  which  translates  the  proper 
gesture  into  words  itacono  amgnapona  tevinitpe,  'one  of  the  other 
hand/  and  so  on  up  to  9.  Coming  to  10,  they  give  it  in  words  as 
amgna  aceponare,  'both  hands/  To  denote  11  they  stretch  out 
both  the  hands,  and  adding  the  foot  they  say  puitta-pona  tevinitpe, 
4  one  to  the  foot/  and  so  on  up  to  15,  which  is  iptaitme,  '  a  whole 


24  A  SHORT  HISTORY  OF  SCIENCE 

foot/  Next  follows  16,  'one  to  the  other  foot/  and  so  on  to  20, 
twin  itoto,  'one  Indian;'  21,  itacono  itoto  jamgnar  bona  tevinitpe, 
'  one  to  the  hands  of  the  other  Indian ' ;  40,  acciache  itoto,  '  two  In- 
dians/ and  so  on  for  60,  80,  100,  '  three,  four,  five  Indians/  and  be- 
yond if  needful.  South  America  is  remarkably  rich  in  such  evidence 
of  an  early  condition  of  finger-counting  recorded  in  spoken  language. 

The  Zulu  counting  on  his  fingers  begins  in  general  with  the  little 
finger  of  his  left  hand.  When  he  comes  to  5,  this  he  may  call  edesanta 
'  finish  hand ; '  then  he  goes  on  to  the  thumb  of  the  right  hand,  and 
so  the  word  tatisitupa  'taking  the  thumb'  becomes  a  numeral  for  6. 
Then  the  verb  komba  'to  point,'  indicating  the  forefinger,  or 
'  pointer/  makes  the  next  numeral,  7.  Thus,  answering  the  question 
'  How  much  did  your  master  give  you  ? '  a  Zulu  would  say  '  U  kom- 
btte'  'He  pointed  with  his  forefinger'  i.e.  'He  gave  me  seven/ 
and  this  curious  way  of  using  the  numeral  verb  is  shown  in  such  an  ex- 
ample as  'amahashi  akombile'  'the  horses  have  pointed'  i.e.  'there 
were  seven  of  them/  In  like  manner,  kijangalobili  'keep  back 
two  fingers/  i.e.  8,  and  kijangalolunje  'keep  back  one  finger'  i.e.  9, 
lead  on  to  kumi,  10 ;  at  the  completion  of  each  ten  the  two  hands  with 
open  fingers  are  clapped  together. 

The  most  instructive  evidence  I  have  found  bearing  on  the  forma- 
tion of  numerals,  other  than  digit-numerals,  among  the  lower  races, 
appears  in  the  use  on  both  sides  of  the  globe  of  what  may  be  called 
numeral-names  for  children.  In  Australia  a  well-marked  case  occurs. 
With  all  the  poverty  of  the  aboriginal  languages  in  numerals,  3  being 
commonly  used  as  meaning  '  several  or  many/  the  natives  in  the  Ade- 
laide district  have  for  a  particular  purpose  gone  far  beyond  this  narrow 
limit,  and  possess  what  is  to  all  intents  a  special  numeral  system,  extend- 
ing perhaps  to  9.  They  give  fixed  names  to  their  children  in  order 
of  age,  which  are  set  down  as  follows  by  Mr.  Eyre:  1,  Kertameru; 
2,  Warritya;  3,  Kudnutya;  4,  Monaitya;  5,  Milaitya;  6,  Marru- 
tya;  7,  Wangutya;  8,  Ngarlaitya;  9,  Pouarna.  These  are  the  male 
names,  from  which  the  female  differ  in  termination.  They  are  given 
at  birth,  more  distinctive  appellations  being  soon  afterwards  chosen. 

The  mathematical  advantage  of  12  as  a  base  conveniently 
divisible  has  often  been  pointed  out,  but  the  choice  unfortunately 
had  to  be  made  long  before  its  real  significance  could  possibly 
be  apprehended,  and  the  difficulty  of  subsequent  change  would  be 


BABYLONIA  AND  EGYPT  25 

prohibitive.  Vestiges  of  the  use  of  5  and  of  20  are  familiar ;  the 
former,  for  example,  in  the  Roman  numerals  IV,  VI,  etc.,  the  latter 
in  such  expressions  as  "three  score  and  ten"  and  in  the  French 
quatre-vingt.  Increasing  maturity  of  a  tribe  or  race,  as  of  an  in- 
dividual, is  accompanied  by  gain  in  the  command  of  larger  and 
larger  numbers,  the  rate  of  progress  being  very  dependent,  however, 
on  a  fortunate  choice  of  notation.  However  great  the  capacity 
for  inventing  number- words,  it  soon  becomes  necessary  to  employ 
some  system  which  shall  lead  to  a  regular  development  of  higher 
from  lower  names.  The  selection  of  a  point  at  which  dependent 
names,  and  later,  symbols  shall  begin,  is  one  of  the  most  important 
steps  in  the  history  of  mathematics.  It  is  difficult  for  us  to 
realize  the  extent  of  our  indebtedness  to  the  comparatively  recent 
so-called  Arabic  —  or  more  properly,  Hindu  —  notation,  in  which 
numbers  of  whatever  magnitude  may  be  expressed  by  means  of 
only  ten  symbols.  In  any  case,  however,  the  appreciation  of 
large  numbers  soon  becomes  vague.  To  most  of  us  the  word 
million  is  nearly  equivalent  to  an  innumerable  multitude. 

PRIMITIVE  GEOMETRY.  —  On  the  geometrical  side  data  are 
naturally  more  meagre.  The  notions  of  a  primitive  society  in 
regard  to  areas  and  perimeters  and  the  ratio  of  a  circumference 
to  its  diameter  may  quite  escape  discovery.  On  the  other  hand 
skill  in  making  and  reading  maps  is  well  known  —  as  among  the 
Esquimaux. 

RELATION  OF  GREEK  TO  OLDER  CIVILIZATIONS.  —  Mathematical 
science  seems  to  have  first  assumed  definite  form  in  Greece,  and  it 
is  of  particular  interest  to  study  the  indebtedness  of  the  Greeks  to 
the  older  civilizations  referred  to  in  the  preceding  chapter.  Some 
degree  of  civilization  doubtless  existed  further  back  than  any  records 
run,  in  China,  in  India,  in  Babylonia,  and  in  Egypt.  But  of  these 
only  the  latter  two  exerted  a  determining  influence  on  the  general 
evolution  of  European  science,  India  making  minor  though  funda- 
mental contributions  at  a  much  later  stage.  Babylonia  and  Egypt 
exchanged  ideas  with  each  other,  and,  after  unnumbered  centuries, 
furnished  Greece  with  a  certain  nucleus  of  scientific  knowledge  of 
which  the  Greeks  made  enormous  use.  In  practical  engineering 


26  A  SHORT  HISTORY  OF  SCIENCE 

the  achievements  of  the  older  civilizations  were  marvellous,  but  for 
the  creation  of  real  science  as  systematized,  organized  knowl- 
edge, containing  within  itself  the  seeds  of  infinite  growth,  they 
were  quite  unequal. 

BABYLONIAN  ARITHMETIC. —  In  Babylonian  arithmetic  whole 
numbers  were  expressed  in  general  by  only  three  of  the  so-called 
cuneiform  or  wedge-shaped  characters  employed  on  the  tablets, 
1  =  Y ,  10  =  -<,  100  =  Y  >-,  but  the  numbers  known  to  have 
been  used  run  into  the  hundred  thousands,  this  naturally  im- 
plying a  highly  developed  command  of  the  fundamental  operations 
by  means  of  which  large  numbers  are  made  to  depend  upon  smaller 
ones.  The  use  of  the  words  for  thousand  and  ten  thousand  in 
characterizing  an  indefinite  multitude  is  illustrated  in  many 
scriptural  passages,  for  example :  "  Saul  hath  slain  his  thousands, 
and  David  his  ten  thousands"  (1  Sam.  xviii.  7);  "a  thousand 
thousands  ministered  unto  him,  and  ten  thousand  times  ten  thou- 
sand stood  before  him"  (Dan.  vii.  10).  With  such  expressions 
may  be  compared :  "  I  will  make  thy  seed  as  the  dust  of  the  earth  " ; 
"He  telleth  the  number  of  the  stars;  he  calleth  them  all  by 
their  names"  (Gen.  xiii.  16;  Ps.  cxlvii.  4).  The  number  40 
also  plays  a  special  role  in  such  expressions  as  the  "forty  years 
in  the  wilderness,"  the  "forty  days  and  forty  nights"  of  rain 
which  caused  the  flood. 

Of  remarkable  interest  in  the  Babylonian  inscriptions  is  the  oc- 
currence, side  by  side  with  a  decimal  system,  of  a  number  system 
based  on  60,  employed  for  mathematical  and  astronomical  pur- 
poses. A  table  of  squares  of  the  natural  numbers  presents,  for 
example,  nothing  novel  for  the  first  seven  numbers,  after  which 
follow,  however,  the  equivalent  of 

1  4    is  the  square  of  8 

1  21  is  the  square  of  9 

1  40  is  the  square  of  10 

2  1    is  the  square  of  11 

Just  as  in  our  notation,  for  example,  325  means  three  times  the 
square  of  ten  plus  twice  ten,  plus  five,  so  this  table  must  mean :  — 


BABYLONIA  AND  EGYPT  27 

once  sixty  plus  four 
once  sixty  plus  twenty-one 
once  sixty  plus  forty 
twice  sixty  plus  one,  etc., 

necessarily  implying  the  representation  of  60  by  1  in  the  second 
place. 

In  a  table  of  cubes,  the  perfect  cube  4096  is  represented  similarly 
by  1  8  16,  that  is'l  X  602  +  8  X  60  +  16  =  4096.  The  origin 
of  this  sexagesimal  system  has  been  ingeniously  attributed  to  the 
blending  of  two  civilizations,  one  possessing  a  system  based  on  10, 
the  other  a  system  based  on  6,  —  a  combination  suggested  by  the 
command  of  the  Persian  king  that  the  Ionian  troops  wait  60 
days  at  the  bridge  over  the  Ister;  by  the  splitting  of  the  river 
by  Cyrus  into  360  rivulets,  etc.  Fractions  were  employed  to  a 
limited  extent  with  denominators  60,  and  3600  (=  60  X  60). 
The  great  step  of  completing  the  number  system  by  a  character 
for  zero  seems  not  to  have  been  successfully  made,  though  there 
are  indications  of  an  approach  to  it  in  later  Babylonian  times. 
There  is  evidence  of  a  mystical  or  magical  use  of  numbers.  Each 
god,  for  example,  was  designated  by  a  number  from  1  to  60  ac- 
cording to  his  rank. 

A  rational  system  of  weights  and  measures  was  introduced, 
the  unit  of  weight  depending  on  that  of  length,  as  in  the  modern 
metric  system. 

BABYLONIAN  ASTRONOMY.  —  In  connection  with  astronomical 
observations  the  Babylonians  invented  a  method  of  measuring 
time  by  means  of  the  water  clock  or  clepsydra.  From  a  vessel 
kept  full,  water  was  allowed  to  escape  very  slowly  into  a  second 
vessel  in  which  it  could  be  weighed.  To  equal  weights  of  water 
corresponded  equal  intervals  of  time. 

Starting  the  flow  at  the  moment  the  upper  edge  of  the  sun 
first  appeared  in  the  east  and  stopping  as  soon  as  the  whole  sun 
was  visible,  the  amount  of  water  collected  was  compared  with 
that  escaping  from  sunrise  to  sunrise,  and  the  sun's  diameter 
thus  determined  as  -^  of  its  whole  path  in  the  sky.  The  time 


28  A  SHORT  HISTORY  OF  SCIENCE 

required  for  traversing  the  whole  path  —  i.e.  the  day  —  was 
then  divided  into  12  double  hours,  in  one  of  which  the  sun's  disk 
advanced  by  its  own  diameter  multiplied  by  60.  Their  use  of 
the  number  60  as  a  base  led  also  to  the  further  subdivision  of  the 
hour  into  60  minutes  of  60  seconds  each.  The  year  was  reckoned 
as  365  days,  and  even  the  unequal  rate  of  the  sun's  motion  at 
different  periods  was  recognized. 

Particularly  noteworthy  in  connection  with  Chaldean  astronomy 
is  the  discovery  of  a  period  of  6585  days,  —  a  little  more  than  18 
years,  —  for  the  recurrence  of  eclipses.  This  would  appear  to  have 
been  based  on  a  long  series  of  observations,  but  to  have  taken  no 
account  of  the  region  of  visibility  of  eclipses  of  the  Sun.  The 
periods  of  the  planets  in  their  orbits  were  approximately  deter- 
mined, but  there  is  no  evidence  of  a  systematic  geometrical 
theory  of  celestial  motions. 

As  to  accuracy  of  direct  observation  it  is  said  that  in  later  Baby- 
lonian times  angles  were  measured  to  within  6  minutes  and  time  to 
less  than  a  minute.  Quantities  obtained  indirectly  by  observa- 
tions extended  over  long  periods,  as  the  length  of  the  lunar  month, 
were  naturally  determined  with  correspondingly  greater  precision. 

A  list  of  eclipses  of  the  moon  from  747  B.C.  was  known  to 
Ptolemy,  while  an  astrological  work  prepared  about  3700  B.C.  con- 
tains evidence  of  a  long  series  of  pre-existing  observations.  To 
the  Romans  the  Chaldeans  were  known  as  star-gazers,  and  the  art 
of  augury  or  divination  was  much  cultivated,  making  some  of  the 
earliest  known  use  of  geometrical  forms.  Herodotus  ascribes  the 
origin  of  the  sun-dial  to  Babylonia. 

BABYLONIAN  GEOMETRY.  —  In  geometry  the  elementary  use  of 
the  circle  quickly  leads  to  the  discovery  that  a  chord  equal  to  the 
radius  subtends  one-sixth  of  the  four  right  angles  at  the  centre,  and 
is  thus  one  side  of  a  regular  inscribed  hexagon,  a  figure  found  on 
Babylonian  monuments.  A  failure  to  distinguish  between  the 
length  of  the  arc  and  that  of  its  chord  led  to  the  first  approximation 
to  the  ratio  of  a  circumference  to  its  diameter,  TT  =  3,  which  occurs 
in  the  Old  Testament  where  King  Solomon's  molten  sea  is  said  to 
be  "ten  cubits  from  the  one  brim  to  the  other:  it  was  round  all 


BABYLONIA  AND  EGYPT  29 

about,  .  .  .  and  a  line  of  thirty  cubits  did  compass  it  round 
about." 

There  is  some  evidence  of  a  knowledge  of  the  fact  that  a  triangle 
of  sides  3,  4,  and  5  has  a  right  angle,  and  the  trisection  of  the  right 
angle  was  accomplished.  The  circle  was  divided  into  360  degrees. 
The  sun-dial  and  its  division  into  degrees  are  very  clearly  men- 
tioned in  the  books  of  Kings  and  Isaiah.  Parallels,  triangles,  and 
quadrilaterals  were  used. 

We  may  summarize  what  we  know  as  to  the  main  features  of 
Babylonian  mathematical  science  as  follows :  — 

In  astronomy,  records  of  observations  extending  over  many  cen- 
turies, the  determination  of  an  18-year  eclipse  period,  the 
approximate  determination  of  the  year  as  365  days,  a  good 
system  of  measuring  time,  the  identification  of  Mercury, 
Venus,  Mars,  Jupiter,  and  Saturn  as  planets ; 

In  arithmetic,  a  well-developed  sexagesimal  system,  tables  of 
squares  and  cubes,  arithmetic  and  geometric  progressions, 
the  use  of  large  numbers ; 

In  geometry,  the  identification  of  the  right  triangle  of  sides 
3,  4,  and  5,  the  inscribed  hexagon,  the  division  of  the  circum- 
ference into  360  degrees,  the  crude  approximation  for  the  ratio 
of  circumference  to  diameter,  TT  =  3. 

MATHEMATICAL  SCIENCE  IN  EGYPT.  —  Josephus  asserts  that 
the  Egyptians  learned  arithmetic  from  Abraham,  who  brought 
it  with  astronomy  from  Chaldea,  and  that  the  Egyptians  in  their 
turn  taught  the  Greeks.  The  indebtedness  of  Greek  science  to 
Egyptians  must  at  any  rate  have  been  very  considerable.  The 
pyramids  are  monumental  evidence  of  appreciation  of  geometric 
form  and  of  a  relatively  high  development  of  engineering  con- 
struction nearly  4000  years  before  the  Christian  era.  Their 
builders  must  have  had  precise  geometrical  and  astronomical 
notions.  In  nearly  all  of  the  pyramids,  for  example,  the  slope 
of  the  lateral  faces  is  52°,  and  the  direction  of  their  base- 
edges  is  nearly  uniform.  The  regular  inscribed  hexagon  was 
known.  After  an  earlier  year  of  12  months  of  30  days  each,  the 


30  A  SHORT  HISTORY  OF  SCIENCE 

Egyptians  added  5  days  at  the  end  of  each  year.  According  to 
their  legend  the  god  Thot  won  these  days  at  play  from  the  moon 
goddess.  An  edict  of  238  B.C.  introduced  the  leap-year,  but  the 
innovation  was  afterwards  forgotten.  The  Egyptian  records 
number  more  than  350  solar,  and  more  than  800  lunar  eclipses 
before  the  Alexandrian  period. 

THE  AHMES  PAPYRUS.  —  Our  most  important  source  of  in- 
formation in  regard  to  early  Egyptian  mathematics  is  the  so-called 
Ahmes  manuscript,  dating  from  some  time  between  1700  and 
2000  B.C.  "Direction for  attaining  knowledge  of  all  dark  things" 
are  the  opening  words  of  this  oldest  known  mathematical  treatise. 
Rules  follow  for  computing  the  capacity  of  barns  and  the  area  of 
fields.  The  text  consists,  however,  rather  of  actual  examples  than 
of  rules,  the  inferring  of  these  being  left  to  the  reader.  Reference 
is  made  to  writings  some  500  years  older,  presumably  based  in 
their  turn  on  centuries  of  tradition. 

In  the  computations  fractions  are  used  as  well  as  whole  numbers, 
but  fractions  other  than  f  are  expressed  in  terms  of  fractions 
with  unit  numerators.  The  problem  of  decomposing  other  frac- 
tions into  a  limited  number  of  such  reciprocals  is  interestingly 
treated,  examples  occurring  of  considerable  complexity.  It 
would  appear  that  such  decompositions,  effected  by  special  de- 
vices or  hit  upon  accidentally,  were  gradually  tabulated  as  rec- 
ords of  mathematical  experiment. 

The  problems  discussed  by  Ahmes  include  a  class  equivalent 
to  our  algebraic  equations  of  the  first  degree  with  one  unknown 
quantity,  —  the  first  known  appearance  of  this  important  idea. 
Thus,  for.  example  :  — 

"Heap  (or  quantity)  its  f ,  its  J,  its  |,  its  whole  makes  33."    In 

o         xx 
our  notation  -a:  +  -  +  -  +  x  =  33. 

o          L       7 

The  solution  requires  the  number  to  be  found  which  multiplying 
1  +  J  4-  \  4-  T  shall  produce  33.  The  result  appears  in  the  suffi- 
ciently intricate  form 


BABYLONIA  AND  EGYPT  31 

Again :  "  Rule  for  dividing  700  loaves  among  four  persons,  f  for 
one,  |  for  the  second,  J  for  the  third,  J  for  the  fourth,  .  .  .  Add 
f ,  |,  |,  and  |  that  gives  1  +  i  +  i  Divide  1  by  1  +  i  +  J  that 
gives  i  +  A.  Make  J  +  ^  of  700  that  is  400."  Thus,  to 
modernize  this  solution,  the  four  persons  A,  B,  C,  and  D  receive 
on  one  round  1  +  i  +  i  =  T  loaves ;  the  number  of  rounds  is 

- j r  or X  700  =  400,  from  which  the  respective 

1+2+4  1+2+4 

shares  are  readily  obtained. 

Certain  problems  show  an  acquaintance  with  arithmetic  and 
geometric  progressions.  Thus,  for  example,  a  series  is  given  of 
the  numbers  7,  49,  343,  2401,  16807,  the  successive  powers  of  7, 
accompanied  by  the  words  person,  cat,  mouse,  barley,  measure. 
Almost  4000  years  later  this  was  interpreted  to  mean :  7  persons 
have  each  7  cats,  each  cat  catches  7  mice,  each  mouse  eats  7  stalks 
of  barley,  each  stalk  can  yield  7  measures  of  grain ;  what  are  the 
numbers  and  what  is  their  sum  ? 

Special  symbols  are  used  for  addition,  subtraction,  and  equality. 
The  Egyptian  seems  never  to  have  had  a  multiplication  table. 
Multiplication  by  13,  for  example,  was  accomplished  by  repeated 
doubling,  and  then  by  adding  to  the  number  itself,  its  products  by 
4  and  by  8. 

Herodotus  reports  from  the  fifth  century  B.C.  that  the  Egyptians 
reckoned  with  stones,  a  practise  independently  developed  in  many 
lands,  notably  in  the  form  of  the  abacus.  This  little  comput- 
ing machine  of  beads  on  wires  was  invented  independently  in 
different  parts  of  the  ancient  world.  In  China  and  other  parts 
of  the  Orient  it  is  still  widely  and  very  skilfully  employed. 

The  handbook  of  Ahmes  is  also  rich  on  the  geometrical  side. 
It  contains  information  in  regard  to  weights  and  measures,  and 
treats  of  the  conversion  from  one  denomination  into  another. 
As  in  case  of  the  progressions,  geometrical  proHems  are  given,  de- 
pending on  the  use  of  formulas  not  derived  in  thatext  itself.  They 
include  computation  of  areas  of  fields  bounded  either  by  straight 
lines  or  circular  arcs,  including  in  the  former  case  owy  isosceles  tri- 
angles, rectangles,  and  trapezoids.  An  isosceles  tr»gle  of  base  4 


32  A  SHORT  HISTORY  OF  SCIENCE 

and  side  10  is  said  to  have  as  its  area  f  X  10  =  20,  the  actual  area 
being  of  course  f  X  V  100—  4(  =  19.6  approximately).  It  is 
interesting  that  this  and  similar  crude  methods  continued  in  use 
by  surveyors  for  many  centuries,  even  after  Euclid  had  given  geo- 
metrical science  its  modern  form.  Another  problem  amounts  to 
finding  two  squares  having  a  given  total  area  and  their  sides  in 
a  given  ratio,  being  thus  equivalent  to  solving  the  equations 


By  trial  x  =  1,  y  =  f,  give  z2  +  i/2  =  (f  )2. 

Since  100  =  (f  )2  X  82,  the  trial  values  must  be  multiplied  by  8, 

so  that  x  =  8  and  y  =  6. 

The  classical  problem  of  "  squaring  the  circle  "  is  attempted,  the 
result  being  equivalent  to  the  approximation  TT  =  ^/f-  =  3.16,  as 
against  the  actual  3.14  —  an  excellent  result  for  the  time. 

Other  computations  deal  with  the  capacity  of  storehouses  —  of 
unknown  shape  —  for  grain.  A  remarkable  group  of  problems 
deals  with  a  certain  geometrical  ratio  in  pyramids  equivalent  to 
a  modern  cosine  or  cotangent,  and  of  interest  in  connection  with 
the  uniform  slope  of  the  great  pyramids. 

EGYPTIAN  LAND  MEASUREMENT.  —  Greek  writers  emphasize 
the  methods  of  land  measurement  of  the  Egyptians  consequent  on 
the  obliteration  of  boundaries  by  floods  of  the  Nile.  Herodotus 
relates  that  Sesostris  had  so  divided  the  land  among  all  Egyptians 
that  each  received  a  rectangle  of  the  same  size,  and  was  taxed  ac- 
cordingly. Whoever  lost  any  of  his  land  by  the  action  of  the  river 
must  report  to  the  king,  who  would*  then  send  an  overseer  to  meas- 
ure the  loss,  and  make  a  proportionate  abatement  of  the  tax. 
Thus  arose  geometry  (geometria  =  earth  measurement).  Dio- 
dorus,  for  example,  says:  "The  Egyptians  claim  to  have  intro- 
duced alphabetical  writing  and  the  observation  of  the  stars,  like- 
wise the  theorems  of  geometry,  and  most  of  the  arts  and  sciences." 
The  priests  "occupy  themselves  busily  with  geometry  and  arith- 
metic, for  as  the  river  annually  changes  the  land,  it  causes  many 
controversies  as^to  boundaries  between  neighbors.  These  cannot 
be  easily  adjusted  unless  a  geometer  ascertains  the  real  facts 


BABYLONIA  AND  EGYPT  33 

by  direct  measurement.  Arithmetic  serves  them  in  domestic 
affairs  and  in  connection  with  the  theorems  of  geometry ;  it  is  also 
of  no  slight  advantage  to  those  who  occupy  themselves  with  the 
stars.  For  if  the  position  and  motions  of  the  stars  have  been  care- 
fully observed  by  any  people  it  is  by  the  Egyptians ;  they  preserve 
records  of  particular  observations  for  an  incredibly  long  series  of 
years.  .  .  .  The  motions  and  times  of  revolution  and  stationary 
points  of  the  planets,  also  the  influence  of  each  on  the  development 
of  living  things  and  all  their  good  and  evil  influences  have  been 
very  carefully  observed  by  them." 

EGYPTIAN  GEOMETRY.  —  In  a  passage  written  about  420  B.C., 
the  Greek  mathematician,  Demoeritus,  boasts  that  "  In  construct- 
ing lines  according  to  given  conditions  no  one  has  ever  surpassed 
me,  not  even  the  so-called  rope-stretchers  of  the  Egyptians." 
The  exact  orientation  of  the  Egyptian  temples  required  the  deter- 
mination of  the  meridian  and  of  a  right  angle.  Both  processes 
were  naturally  an  important  part  of  the  mathematical  lore  of  the 
priesthood.  The  first  step  was  accomplished  by  observation  of 
the  stars.  It  is  believed  that  the  second  step  was  the  function  of 
the  "rope-stretchers,"  the  name  being  due  to  their  dependence  on  a 
rope  of  length  12,  divided  by  two  knots  into  sections  of  3,  4,  and  5. 
When  the  two  ends  of  the  rope  are  joined  and  the  three  sections 
drawn  taut  by  the  knots,  the  angle  opposite  the  section  5  is  a  right 
angle.  The  geometrical  knowledge  thus  attributed  to  the  Egyp- 
tians of  a  special  case  of  the  Pythagorean  proposition  does  not,  of 
course,  imply  knowledge  of  the  proposition  itself,  or  even  the  ability 
to  prove  the  particular  case,  which  was  probably  known  only  em- 
pirically. Egyptian  architecture  made  use  of  geometrical  figures 
as  wall  decoration  and  even  employed  the  principle  of  propor- 
tionality, by  dividing  a  blank  wall-space  into  squares  before  apply- 
ing the  design.  The  idea  of  perspective  drawing  seems,  however, 
not  to  have  been  attained. 

The  existence  of  such  a  problem  book  as  that  of  Ahmes  may  be 
considered  as  fairly  implying  also  the  existence  of  comparable 
treatises  of  a  more  theoretical  character,  but  other  evidence  of  this 
is  lacking. 


34 


A  SHORT  HISTORY  OF  SCIENCE 


The  main  features  of  Egyptian  mathematical  science  are  then 
as  follows :  about  2000  B.C.  a  well-developed  use  of  whole  numbers 
and  fractions ;  a  method  of  solving  equations  of  the  first  degree 
with  one  unknown  quantity;  an  approximate  method  for  find- 
ing the  circumference  of  a  circle  of  given  radius;  approximate 
methods  for  finding  areas  of  isosceles  triangles  and  trapezoids; 
the  rudiments  of  a  theory  of  similar  figures. 

REFERENCES  FOR  READING 

BALL.  A  Short  History  of  Mathematics,  Chapter  I.  GAJORI.  A  History  of 
Mathematics,  pages  1-15.  BERRY.  A  History  of  Astronomy,  Chapter  I. 
DREYER.  Planetary  Systems,  Introduction.  Gow.  History  of  Greek  Mathe- 
matics, Chapters  I,  II. 


,*t$    of    the 


MAP  OF  THE  WORLD  BY  HBCAT^JUS  (517  B.C.) 
(From  Breasted's  Ancient  Times.    Courtesy  of  Messrs.  Ginn  &  Co.) 

Hecatseua,  a  geographer  of  Miletus,  travelled  widely,  including  a  journey  up  the  Nile,  and 
wrote  a  geography  of  the  world.  In  this  book,  as  in  the  Map  .  .  .  the  Mediterranean  Sea  was 
the  centre  and  the  lands  about  it  were  all  those  known  to  the  author.  .  .  .  After  the  Unknown 
Historian  of  the  Hebrews  [about  850  B.C.]  he  was  the  first  historical  writer  of  the  early  world. 


CHAPTER  III 

THE  BEGINNINGS  OF  SCIENCE  IN  GREECE 

Except  the  blind  forces  of  Nature  nothing  moves  in  this  world 
which  is  not  Greek  in  its  origin.  —  Sir  Henry  Sumner  Maine. 

A  spirit  breathed  of  old  on  Greece  and  gave  birth  to  poets  and 
thinkers.  There  remains  in  our  classical  education  I  know  not  what 
of  the  old  Greek  soul  —  something  that  makes  us  look  ever  upward. 
And  this  is  more  precious  for  the  making  of  a  man  of  science  than  the 
reading  of  many  volumes  of  geometry.  —  Poincare. 

Number,  the  inducer  of  philosophies, 
The  synthesis  of  letters.  —  Mschylus. 

Mathematics,  considered  as  a  science,  owes  its  origin  to  the  idealistic 
needs  of  the  Greek  philosophers,  and  not  as  fable  has  it,  to  the  practical 
demands  of  Egyptian  economics.  .  .  .  Adam  was  no  zoologist  when 
he  gave  names  to  the  beasts  of  the  field,  nor  were  the  Egyptian  sur- 
veyors mathematicians.  —  Hankel. 

GEOGRAPHICAL  BOUNDARIES.  —  From  the  twilight  of  civili- 
zation and  the  first  faint  suggestions  of  science  in  Chaldea  and 
Egypt,  we  pass  to  the  more  brilliant  dawn  of  science  and  civili- 
zation in  Greece.  Geographically  we  shall  be  concerned  not 
merely  with  Greece  itself,  but,  as  time  passes,  with  other  Hellenic 
countries,  especially  the  Ionian  shores  and  islands  of  western 
Asia  Minor,  and  the  Greek  colonies  in  southern  Italy,  Sicily,  and, 
after  its  conquest  by  Alexander  the  Great,  northern  Egypt.  Greece 
and  its  civilization  seem  immeasurably  closer  to  us  both  in  time 
and  in  spirit  than  do  ancient  Babylonia  and  Egypt.  In  these 
more  remote  civilizations  science  had  been  cultivated  chiefly  as  a 
tool,  either  for  immediate  practical  applications  or  as  a  part  of  the 
professional  lore  of  a  conservative  priesthood.  In  Greece,  on 
the  other  hand,  for  the  first  time  in  the  history  of  our  race, 

35 


36  A  SHORT  HISTORY  OF  SCIENCE 

human  thought  achieved  freedom,  and  real  science  became  pos- 
sible. 

Mathematics  as  a  science  commenced  when  first  some  one,  prob- 
ably a  Greek,  proved  propositions  about  any  things  or  about  some 
things,  without  specification  of  definite  particular  things.  —  White- 
head. 

INDEBTEDNESS  OF  GREECE  TO  BABYLONIA  AND  EGYPT.  —  It  is 
plain,  nevertheless,  that  Greek  civilization  and  Greek  science 
owed  much  to  Egypt  and  Chaldea.  Herodotus  has  been  quoted 
already,  and  Theon  of  Smyrna  (second  century  A.D.)  says  :  — 

In  the  study  of  the  planetary  movements  the  Egyptians  had 
employed  constructive  methods  and  drawing,  while  the  Chaldeans 
preferred  to  compute,  and  to  these  two  nations  the  Greek  astrono- 
mers owed  the  beginnings  of  their  knowledge  of  the  subject. 

Again  in  the  third  century  A.D.  Porphyry  observes :  — 

From  antiquity  the  Egyptians  have  occupied  themselves  with 
geometry,  the  Phoenicians  with  numbers  and  reckoning,  the  Chal- 
deans with  theorems. 

THE  GREEK  POINT  OF  VIEW.  —  It  is  not,  however,  so  much  the 
achievements  of  the  Greeks  in  positive  science  which  compel  our 
attention  and  admiration  as  it  is  the  remarkable  spirit  which  they 
displayed  toward  man  and  the  universe.  Here  for  the  first  time 
we  meet  with  a  new  point  of  view,  and  while  Shelley's  well-known 
dictum,  "  We  are  all  Greeks,  our  laws,  our  literature,  our  religion, 
our  art  have  their  roots  in  Greece,"  must  IDC  dismissed  as  in- 
correct as  well  as  extravagant,  and  even  Sir  Henry  Maine's 
maxim,  which  stands  at  the  head  of  this  chapter,  is  undoubtedly 
an  exaggeration,  these  famous  sayings  serve  well  to  illustrate 
the  fact  that  with  the  Greeks  came  into  the  world  a  new 
spirit  and  a  new  interpretation  of  Nature. 

In  a  striking  essay  entitled  "What  we  owe  to  Greece,"  Butcher 
has  portrayed  with  extraordinary  clearness  those  characteristics 
of  the  Greeks  which  lifted  them  above  all  of  their  predecessors  and 
above  most  if  not  all  of  those  that  have  come  after  them :  — 


BEGINNINGS  IN  GREECE  37 

The  Greeks  before  any  other  people  of  antiquity  possessed  the 
love  of  knowledge  for  its  own  sake.  To  see  things  as  they  really  are, 
to  discern  then*  meaning  and  adjust  their  relations,  was  with  them 
an  instinct  and  a  passion.  Their  method  in  science  and  philosophy 
might  be  very  faulty  and  their  conclusions  often  absurd,  but  they 
had  that  fearlessness  of  intellect  which  is  the  first  condition  of  seeing 
truly.  .  .  -  Greece,  first  smitten  with  the  passion  for  truth,  had 
the  courage  to  put  faith  in  reason  and  in  following  its  guidance  to 
take  no  account  of  consequences.  'Those/  says  Aristotle,  'who 
would  rightly  judge  the  truth  must  be  arbitrators  and  not  litigants.' 
'Let  us  follow  the  argument  wheresoever  it  leads'  may  be  taken 
not  only  as  the  motto  of  the  Platonic  philosophy  but  as  expressing  one 
side  of  the  Greek  genius 

At  the  moment  when  Greece  has  come  into  the  main  current  of 
the  world's  history,  we  find  a  quickened  and  stirring  sense  of  per- 
sonality and  a  free  people  of  intellectual  imagination.  The  oppres- 
sive silence  with  which  Nature  and  her  unexplained  forces  had  brooded 
over  man  is  broken.  Not  that  the  Greek  temper  is  irreverent  or 
strips  the  universe  of  mystery.  The  mystery  is  still  there  and  felt  .  .  . 
but  the  sense  of  mystery  has  not  yet  become  mysticism.  .  .  .  Greek 
thinkers  are  not  afraid  lest  they  should  be  guilty  of  prying  into  hidden 
things  of  the  gods.  They  hold  frank  companionship  with  thoughts 
that  had  paralyzed  Eastern  nations  into  dumbness  or  inactivity,  and 
in  their  clear  gaze  there  is  no  ignoble  terror.  .  .  .  Know  thyself,  is 
the  answer  which  the  Greek  offers  to  the  sphinx's  riddle.  .  .  .  But 
to  the  Greeks,  'know  thyself  meant  not  only  to  know  man  but  the 
less  pleasing  task  to  know  foreigners.  .  .  .  The  people  of  ancient 
India  did  not  care  to  venture  beyond  their  mountain  barriers  and  to 
know  their  neighbors.  The  Egyptians,  though  in  certain  branches  of 
science  they  had  made  progress,  —  in  medicine,  in  geometry,  in  as- 
tronomy, —  had  acquired  no  scientific  distinction  for  they  kept  to 
themselves,  but  the  Greeks  were  travellers.  .  .  .  Aristotle  thought 
it  worth  his  while  to  analyze  and  describe  the  constitutions  of  58 
states,  including  in  his  survey  not  only  Greek  states  but  those  of  the 
barbarian  world.  .  .  . 

It  was  the  privilege  of  the  Greeks  to  discover  the  sovereign  efficacy 
of  reason.  .  .  .     And  it  was  Ionia  that  gave  birth  to  the  idea  which    , 
was  foreign  to  the  East  but  has  become  the  starting-point  of  modern 
science,  the  idea  that  Nature  works  by  fixed  laws.  .  .  .     Again,  in 


38  A  SHORT  HISTORY  OF  SCIENCE 

history  the  Greeks  were  the  first  who  combined  science  and  art,  reason 
and  imagination.  .  .  .  The  application  of  a  clear  and  fearless  intel- 
lect to  every  domain  of  Me  was  one  of  the  services  rendered  by  Greece 
to  the  world.  It  was  connected  with  an  awakening  of  the  lay  spirit. 
In  the  East  the  priests  had  generally  held  the  keys  of  knowledge.  .  .  . 
To  Greece  then  we  owe  the  love  of  science,  the  love  of  art,  the  love  of 
freedom.  .  .  .  And  in  this  union  we  recognize  the  distinctive  features 
of  the  West.  The  Greek  genius  is  the  European  genius  in  its  first 
and  brightest  bloom. 

SOURCES.  —  The  sources  of  our  information  as  to  the  details  of 
the  scientific  ideas  of  the  Greeks  are  exceedingly  meagre,  some  of 
the  most  important  historical  and  scientific  treatises  being  known 
to  us  only  by  title  or  by  detached  quotations,  or  indirectly  through 
Arabic  translations.  Among  specific  ancient  sources  of  infor- 
mation in  regard  to  Greek  mathematical  science  the  following 
may  be  mentioned :  — 

About  330  B.C.,  Eudemus,  a  disciple  of  Aristotle,  wrote  a  his- 
tory of  geometry  of  which  a  summary  by  Proclus  has  been 
preserved. 

About  70  B.C.,  Geminus  of  Rhodes  wrote  an  Arrangement  of 
Mathematics  with  historical  data.  This  has  also  been  lost,  but 
quotations  are  preserved  in  some  of  the  later  authors. 

About  140  A. D.,  Theon  of  Smyrna  wrote  Mathematical  Rules 
necessary  for  the  Study  of  Plato. 

About  300  A.D.,  Pappus'  Collections  contain  much  information 
in  regard  to  the  previous  development  of  geometry. 

In  the  fifth  century  A.D.,  Proclus  published  a  commentary  on 
Euclid's  Elements  with  valuable  historical  data. 

THE  CALENDAR.  —  The  Greek  calendar  was  based  at  an  early 
period  on  the  lunar  month,  the  year  consisting  of  12  months  of 
30  days  each.  About  600  B.C.  a  correction  was  made  by  Solon, 
making  every  two  years  contain  13  months  of  30  days  and  12  of 
29  days  each,  giving  thus  369  days  per  year.  In  the  following 
century  a  much  closer  approximation  —  365|  days  —  was  at- 
tained by  confining  the  thirteenth  month  to  three  years  out  of 
eight.  This  arrangement  naturally  failed,  however,  to  meet  the 


BEGINNINGS  IN  GREECE  39 

Greek  desire  that  the  months  begin  regularly  at  or  near  new  moon, 
and  Aristophanes  makes  the  Moon  complain: 

CHORUS  OF  CLOUDS 

"  The  Moon  by  us  to  you  her  greeting  sends, 
But  bids  us  say  that  she's  an  ill-used  moon, 
And  takes  it  much  amiss  that  you  should  still 
Shuffle  her  days,  and  turn  them  topsy-turvy ; 
And  that  the  gods  (who  know  their  feast-days  well,) 
By  your  false  count  are  sent  home  supperless, 
And  scold  and  storm  at  her  for  your  neglect." 

About  400  B.C.,  Meton  the  Athenian  observed  that  19  years 
consist  of  almost  exactly  235  lunar  months,  and  accordingly  pro- 
posed a  new  calendar  with  125  months  of  30  days  and  110  of  29 
days,  corresponding  to  an  average  year  of  365  days,  6  hours  and 
19  minutes  —  only  about  30  minutes  too  long.  Of  this  Meton's 
cycle  the  traditional  rule  for  determining  the  date  of  Easter  still 
preserves  traces.  On  account  of  so  much  confusion  in  the  official 
calendar  the  almanacs  of  the  time  even  designated  the  dates  for 
agricultural  operations  by  means  of  the  constellations  visible  at 
the  corresponding  time. 

TIME  MEASUREMENT.  —  While  sun  and  moon  suffice  for  large- 
scale  measurement  of  time,  the  approximate  determination  of  its 
subdivisions  early  became  important,  and  this  problem  has  been 
solved  with  continually  increasing  precision  to  our  own  day. 
Early  time  measurement  depended  either  on  some  form  of  sun- 
dial as  a  natural  means,  or  on  an  apparatus  analogous  to  the 
hour-glass  as  an  artificial  method. 

In  Isaiah  xxxviii.  8,  in  connection  with  a  promise  of  prolonged 
life  to  Hezekiah,  it  is  said 

And  this  shall  be  a  sign  unto  thee  from  the  Lord,  that  the  Lord 
will  do  this  thing  that  he  hath  spoken ;  behold,  I  will  bring  again  the 
shadow  of  the  degrees,  which  is  gone  down  in  the  sun-dial  of  Ahaz, 
ten  degrees  backward.  So  the  sun  returned  ten  degrees,  by  which 
degrees  it  was  gone  down. 


40  A  SHORT  HISTORY  OF  SCIENCE 


The  first  sun-dial  of  which  a  description  is  preserved  belongs  to 
the  time  of  Alexander  the  Great,  and  consisted  of  a  hollow  hemi- 
sphere with  its  rim  horizontal  and  a  bead  at  the  centre  to  cast  the 
shadow.  Curves  drawn  on  the  concave  interior  divided  the  period 
from  sunrise  to  sunset  into  twelve  parts,  these  lengths  being  thus 
proportionate  to  the  lengths  of  the  daylight  period. 

The  use  of  the  clepsydra,  or  water  clock,  in  Greece  dates  from  the 
fifth  century  B.C.  It  consisted  there  of  a  spherical  bottle  with  a 
minute  outlet  for  the  gradual  escape  of  water.  Its  use  in  regulat- 
ing public  speaking  is  illustrated  by  Demosthenes'  demand  when 
interrupted,  "You  there :  stop  the  water." 

For  the  sake  of  conformity  with  the  sun-dial  division  of  each 
day  and  each  night  into  twelve  equal  parts,  the  rate  of  flow  in  the 
clepsydra  required  continual  adjustment.  Ingenious  improvements 
were  made  in  the  mechanism  in  course  of  time,  but  in  considering 
the  work  of  the  Greek  astronomers,  the  impossibility  of  what  we 
should  consider  accurate  time  measurement  must  not  be  for- 
gotten. 

GREEK  ARITHMETIC.  —  In  Greek  arithmetic  the  earliest  known 
numerals  are  merely  the  initials  of  the  respective  number  wprds. 
Two  other  systems  came  into  use  later.  In  one  of  these  the 
numbers  from  1  to  24  are  represented  by  the  24  letters  of  the 
Ionian  alphabet ;  in  the  other  the  letters  represent  numbers,  but 
no  longer  in  consecutive  order.  This  use  of  letters  for  numbers 
was  not  confined  to  Greece,  but  appears  to  have  originated  there. 
The  Greeks  had  no  zero,  and  never  discovered  the  immense  ad- 
vantage of  a  position-system,  such  as  that  by  which  we  are  able 
to  express  all  numbers  by  only  ten  symbols.  Fractions  occur  not 
infrequently.  The  change  from  the  earlier  notation  to  that  with 
24  characters  was  a  disastrous  one.  There  were  not  only  more 
characters  to  memorize,  but  computation  became  materially  more 
complicated.  These  disadvantages  far  more  than  offset  the  su- 
perior compactness,  the  sole  merit  of  the  new  system.  The 
special  importance  of  such  compactness  for  coins  has  led  to  the 
suggestion  that  they  were  the  medium  through  which  this  nota- 
tion was  introduced. 


BEGINNINGS  IN  GREECE  41 

A  simple  numerical  computation  of  late  date  in  the  Greek 
alphabetic  numerals  and  its  modern  equivalent  are 


265 
265 


s     a  40  000,     12  000,  1000 

M  M    t/3   ,a 

a 

M   ,0   ,7  %  T  12  000,      3  600,    300 

ja     T  Jre  1  OOP,          300,     25 

I      70  225 

M     a-    K  e 

—  Gow. 

Division  was  an  exceedingly  laborious  process  of  repeated  sub- 
traction. 

Probably  nothing  in  the  modern  world  would  have  more  aston- 
ished a  Greek  mathematician  than  to  learn  that,  under  the  influence 
of  compulsory  education,  the  whole  population  of  Western  Europe, 
from  the  highest  to  the  lowest,  could  perform  the  operation  of  division 
for  the  largest  numbers.  —  Whitehead. 

Approximate  square  roots  were  found  by  the  later  Greeks. 
Theon  in  the  fourth  century  A.D.  for  example  gives  the  following 
rule :  — 

When  we  seek  a  square-root,  we  take  first  the  root  of  the  nearest 
square-number.  We  then  double  this  and  divide  with  it  the  re- 
mainder reduced  to  minutes  and  subtract  the  square  of  the  quotient, 
then  we  reduce  the  remainder  to  seconds  and  divide  by  twice  the 
degrees  and  minutes  (of  the  whole  quotient).  We  thus  obtain  nearly 
the  root  of  the  quadratic. 

The  reckoning  board,  or  abacus,  —  known  in  so  many  different 
forms  throughout  the  world,  —  came  into  very  early  use,  but 
actual  evidence  in  regard  to  its  form  is  meagre.  A  sharp  dis- 
tinction was  made  between  the  art  of  calculation  (logistica),  and 
the  science  of  numbers  (arithmetica) .  The  former  was  deemed 
unworthy  the  attention  of  philosophers,  and  to  their  attitude  may 
be  fairly  attributed  the  fact  that  Greek  mathematics  was  always 


42  A  SHORT  HISTORY  OF  SCIENCE 

weak  on  the  analytical  side,  and  seemed  in  a  few  centuries  to 
reach  the  limit  of  its  possible  development. 

GREEK  GEOMETRY.  —  It  was  in  geometry  that  Greek  mathe- 
matics chiefly  developed,  and  for  several  fundamental  reasons. 
The  Greek  mind  had  a  strong  predilection  for  formal  logic,  a  keen 
aesthetic  appreciation  of  beauty  of  form,  and,  on  the  other  hand, 
with  no  adequate  symbolism  for  arithmetic  or  algebra,  a  distinct 
disdain,  at  any  rate  among  the  educated,  for  the  commercialized 
mathematics  of  computation.  The  history  of  Greek  mathematics 
is  therefore  to  a  great  extent  the  history  of  geometry.  Formal 
geometry  as  distinguished  from  the  solving  of  particular  geo- 
metrical problems,  had,  indeed,  no  previous  existence,  and  we 
have  to  do  with  the  beginnings  of  elementary  geometry  as  we  now 
know  it. 

THE  IONIAN  PHILOSOPHERS.  —  The  sense  of  curiosity,  the  feel- 
ing of  wonder,  the  spirit  of  inquiry,  —  these  are  the  common  ele- 
ments of  philosophy  and  science.  It  is  thus  not  strange  that  the 
earliest  names  in  science  are  likewise  the  earliest  in  philosophy. 

In  the  childhood  and  youth  of  the  race  specialization  has  not 
begun,  all  knowledge  lies  invitingly  open  to  the  expanding  mind. 
We  have  seen  how  much  had  been  accumulated  in  Egypt  and 
Babylonia  of  knowledge  and  skill  in  observing  and  recording  the 
phenomena  of  the  heavens,  in  irrigation  and  in  measurement  of 
land.  Much  of  the  same  general  character  was  doubtless  true  of 
the  Phoenicians,  the  Trojans,  the  Cretans,  and  other  precursors  of 
the  Greeks.  But  nothing  deserving  the  name  of  science  has  come 
down  to  us  from  the  ^Egean  or  Greek  civilization  before  the  time 
of  Thales  of  Miletus,  chief  of  the  Ionian  philosophers,  and  one 
of  the  "  seven  wise  men  of  Greece." 

THALES.  —  The  ancient  and  fragmentary  register  of  Greek 
mathematicians,  or  history  of  Greek  geometry  before  Euclid, 
attributed  to  Eudemus,  begins : 

As  it  is  now  necessary  to  consider  also  the  beginnings  of  the  arts 
and  sciences  in  the  present  period,  we  report  that,  according  to  the 
evidence  of  most,  geometry  was  invented  by  the  Egyptians,  taking 
its  origin  from  the  measurement  of  land.  This  last  was  necessary 


BEGINNINGS  IN  GREECE  43 

for  them  on  account  of  the  inundation  of  the  Nile,  which  obliterated 
every  man's  boundaries.  It  is  however,  nothing  wonderful  that  the 
invention  of  this  as  of  the  other  sciences  has  grown  out  of  necessity, 
as  everything  in  its  beginnings  proceeds  from  the  incomplete  to  the 
complete.  A  regular  transition  takes  place  from  perception  to  thought- 
ful consideration,  from  this  to  rational  knowledge.  Just  as  now  with 
the  Phoenicians  an  exact  knowledge  of  numbers  took  its  rise  in  the 
needs  of  trade  and  commerce,  so  geometry  began  with  the  Egyptians 
for  the  reason  mentioned.  Thales,  who  went  to  Egypt,  first  brought 
this  science  into  Greece.  Much  he  discovered  himself,  of  much 
however  he  transmitted  the  beginnings  to  his  successors.  Some 
things  he  made  more  general,  some  more  comprehensible. 

The  significance  packed  into  this  terse  quotation  may  well  be 
emphasized.  The  mathematics  of  the  Chaldeans,  the  Egyptians, 
the  Phoenicians,  was  merely  a  tool,  crudely  shaped  to  meet  vital 
concrete  needs;  it  had  little  possibility  of  development.  The 
Greek  intellect,  seizing  upon  the  fragmentary  knowledge  of  these 
practical  races,  refined  from  it  the  germs  of  a  new  pure  science, 
making  the  knowledge  "more  general"  and  "more  comprehen- 
sible," and  at  the  same  time  discovering  much  that  was  new.  On 
the  other  hand,  inclining  in  its  zeal  for  pure  science  to  the  op- 
posite extreme  of  disregard  for  the  concrete  applications,  Greek 
science  eventually  reached  its  own  limit  of  possible  growth.  In 
the  long  run  scientific  progress  must  depend  on  due  appreciation 
of  the  complementary  importance  of  both  pure  and  applied  science. 

Thales  was  of  Phoenician  descent,  and  was  born  about  624  B.C. 
in  Miletus,  a  city  of  Ionia,  at  that  time  a  flourishing  Greek  colony 
in  what  is  now  Asia  Minor.  As  an  engineer  he  was  employed  to 
construct  an  embankment  for  the  river  Halys.  As  a  merchant 
he  dealt  in  salt  and  oil,  and,  visiting  Egypt,  learned  there 
something  of  the  wisdom  of  the  Egyptian  priesthood.  He  oc- 
cupied himself  with  the  study  of  the  stars  as  well  as  of  geometry, 
and  in  particular, 

announced  to  the  inhabitants  of  Miletus  that  night  would  enter 
upon  the  day,  the  sun  hide  himself,  the  moon  place  herself  in  front, 
so  that  his  light  and  radiance  would  be  intercepted. 


44  A  SHORT  HISTORY  OF  SCIENCE 

Herodotus  says  that  there  was  a  war  between  the  Lydians  and 
the  Medes,  and  after  various  turns  of  fortune 
in  the  sixth  year  a  conflict  took  place,  and  on  the  battle  being  joined, 
it  happened  that  the  day  suddenly  became  night.  And  this  change, 
Thales  of  Miletus  had  predicted  to  them,  definitely  naming  this  year, 
in  which  the  event  really  took  place.  The  Lydians  and  the  Medes, 
when  they  saw  the  day  turned  into  night,  ceased  from  fighting,  and 
both  sides  were  desirous  of  peace. 

This  eclipse  is  supposed  to  have  taken  place  in  585  B.C.  The 
prediction  of  the  year  of  an  eclipse  gained  Thales  a  great  repu- 
tation with  his  contemporaries,  though  his  designation  with  six 
others  as  "wise  men  of  Greece"  appears  to  have  had  a  primarily 
political  significance.  None  of  the  other  six  at  any  rate  had  any 
scientific  standing.  He  taught  that  the  year  has  365  days ;  that 
the  equinoxes  divide  the  year  unequally;  that  the  moon  is  illu- 
minated by  the  sun.  The  mathematical  attainments  attributed 
to  Thales  include  the  following  theorems  of  elementary  geometry ; 
the  angles  at  the  base  of  an  isosceles  triangle  are  equal ;  when  two 
straight  lines  cut  each  other  the  opposite  angles  are  equal;  the 
first  proof  that  the  circle  is  bisected  by  its  diameter;  the  in- 
scription of  the  right  triangle  in  the  semicircle ;  the  measurement 
of  height  by  shadow,  involving  the  principle  of  similar  triangles. 

Plutarch  relates  that  Niloxenus,  conversing  with  Thaies  con- 
cerning King  Amasis,  says :  — 

Although  he  also  admires  you  on  account  of  other  things,  he 
prizes  above  everything  the  measurement  of  the  pyramids,  in  that 
you  have  without  any  trouble  and  without  needing  an  instrument, 
merely  placed  your  staff  at  the  end  of  the  shadow  cast  by  the  pyramid, 
showing  from  the  two  triangles  formed  by  the  contact  of  the  solar 
rays  that  one  shadow  lias  the  same  relation  to  the  other  as  the  pyra- 
mid to  the  staff. 

Some  writers  even  attribute  to  Thales  a  knowledge  that  the 
sum  of  the  angles  of  a  triangle  is  two  right  angles,  also  of  the 
idea  of  a  circle  as  a  locus  of  a  point  having  a  certain  property, 
but  conclusive  evidence  can  hardly  be  adduced.  Even  the  im- 


BEGINNINGS  IN  GREECE  45 

plied  knowledge  of  similar  triangles  is  doubtful.  In  connection 
with  his  shadow  measurements  it  is  interesting  that  his  scholar 
Anaximander,  born  611  B.C.,  introduced  the  sun-dial  into  Greece. 

While  our  knowledge  of  Thales  and  his  work  is  extremely 
meagre,  the  mathematical  results  above  mentioned  have  consid- 
erable significance  in  connection  with  the  comparison  between 
Greece  and  Egypt.  The  Egyptian  standpoint  was  fundamentally 
practical,  specific,  inductive;  the  Greek  shows  already  its  char- 
acteristic tendencies  to  abstract  generalization,  to  logical  proof, 
and  to  the  methods  of  deductive  science.  Most  of  the  facts  as- 
cribed to  Thales  may  well  have  been  known  to  the  Egyptians. 
For  them  these  facts  would  have  remained  unrelated;  for  the 
Greeks  they  were  the  beginnings  of  an  extraordinary  develop- 
ment of  the  science  of  geometry. 

MILESIAN  COSMOLOGY.  —  The  cosmological  ideas  of  the  Milesian 
philosophers  were  sufficiently  ingenious  and  picturesque.  To 
Thales  the  earth  is  a  circular  disk  floating  in  an  ocean  of  water. 
This  water  is  the  fundamental  element  of  the  whole.  Ice,  snow, 
and  frost  turn  readily  into  water,  even  rocks  wear  away  and 
disappear  in  it.  Man  himself  seems  capable  of  turning  into  it, 
while  the  waters  of  sea  and  land  shrink  into  solid  residues.  By 
evaporation  of  the  water  air  is  formed,  its  agitation  causes  earth- 
quakes. The  stars  between  their  setting  and  rising  pass  behind 
the  earth. 

The  following  passages  (Fairbanks'  translation)  indicate  the 
estimation  in  which  Thales  was  held  by  later  Greek  philosophers. 

As  to  the  quantity  and  form  of  this  first  principle  or  element, 
there  is  a  difference  of  opinion ;  but  Thales,  the  founder  of  this  sort 
of  philosophy,  says  that  it  is  water  (accordingly  he  declares  that  the 
earth  rests  on  water),  getting  the  idea  I  suppose  because  he  saw  that 
the  nourishment  of  all  beings  is  moist,  and  that  warmth  itself  is 
generated  from  moisture  and  persists  in  it  (for  that  from  which  all 
things  spring  is  the  first  principle  of  them) ;  and  getting  the  idea  also 
from  the  fact  that  the  germs  of  all  beings  are  of  a  moist  nature,  while 
water  is  the  first  principle  of  the  nature  of  what  is  moist.  .  .  . 
'Some  say  that  the  earth  rests  on  water.  I  have  ascertained  that 


46  A  SHORT  HISTORY  OF  SCIENCE 

the  oldest  statement  of  this  character  is  the  one  credited  to  Thales, 
the  Milesian,  to  the  effect  that  it  rests  on  water,  floating  like  a  piece 
of  wood  or  something  else  of  that  sort.'  .  .  .  And  Thales,  according 
to  what  is  related  of  him,  seems  to  have  regarded  the  soul  as  some- 
thing endowed  with  the  power  of  motion,  if  indeed  he  said  that  the 
loadstone  has  a  soul  because  it  moves  iron.  .  .  .  Some  say  that  soul  is 
diffused  throughout  the  whole  universe;  and  it  may  have  been  this 
which  led  Thales  to  think  that  all  things  are  full  of  gods. — Aristotle. 

Of  those  who  say  that  the  first  principle  is  one  and  movable,  to 
whom  Aristotle  applies  the  distinctive  name  of  physicists,  some  say 
that  it  is  limited;  as  for  instance  Thales  of  Miletos  .  .  .  who 
seems  also  to  have  lost  belief  in  the  gods.  These  say  that  the  first 
principle  is  water,  and  they  are  led  to  this  result  by  things  that  appear 
to  the  senses ;  for  warmth  lives  in  moisture  and  dead  things  wither 
up  and  all  germs  are  moist  and  all  nutriment  is  moist  ....  Thales 
is  the  first  to  have  set  on  foot  the  investigation  of  nature  by  the 
Greeks ;  although  so  many  others  preceded  him,  he  so  fai  surpassed 
them  as  to  cause  them  to  be  forgotten.  It  is  said  that  he  left  nothing 
in  writing  except  a  book  entitled  Nautical  Astronomy.  —  Theo- 
phrastw. 

It  is  said  that  Thales  of  Miletos,  one  of  the  seven  wise  men,  was 
the  first  to  undertake  the  study  of  Physical  Philosophy.  He  said 
that  the  beginning  (the  first  principle)  and  the  end  of  all  things  is 
water.  All  things  acquire  firmness  as  this  solidifies,  and  again,  as  it 
melts,  their  existence  is  threatened ;  to  this  are  due  earthquakes  and 
whirlwinds  and  movements  of  the  stars  ....  Thales  was  the  first 
of  the  Greeks  to  devote  himself  to  the  study  and  investigation  of  the 
stars  and  was  the  originator  of  this  branch  of  science ;  on  one  occa- 
sion he  was  looking  up  at  the  heavens  and  was  just  saying  he  was  in- 
tent on  studying  what  was  overhead,  when  he  fell  into  a  well ;  where- 
upon a  maid-servant  named  Thratta  laughed  at  him  and  said :  '  In 
his  zeal  for  things  in  the  sky  he  does  not  see  what  is  at  his  feet.'  And 
he  lived  in  the  time  of  Krcesos.  —  Hippolytus. 

Thales  of  Miletos  regards  the  first  principle  and  the  element  as 
the  same  thing.  ...  So  we  call  earth,  water,  air,  fire,  elements.  .  .  . 
Thales  declared  that  the  first  principle  of  things  is  water.  The 
Physicists,  followers  of  Thales,  all  recognize  that  the  void  is  really  a 
void.  The  earth  is  one  and  spherical  in  form.  It  is  in  the  midst 
of  the  universe.  Thales  and  Democritus  find  in  water  the  cause 


BEGINNINGS  IN  GREECE  47 

of  earthquakes.  .  .  .  Thales  thinks  that  the  Etesian  winds  blowing 
against  Egypt  raise  the  mass  of  the  Nile,  because  its  outflow  is  beaten 
back  by  the  swelling  of  the  sea  which  lies  over  its  mouth.  —  Mtius. 

ANAXIMANDER.  —  A  second  native  of  Miletus,  Anaximander 
(about  611-545  B.C.)  had  a  different  interpretation  of  nature, 
holding  that  the  fundamental  stuff,  out  of  which  all  things  are 
made,  is  something  between  air  and  water.  He  believed  the  earth 
to  be  balanced  in  the  centre  of  the  world,  because  being  in  the 
centre  and  having  the  same  relation  to  all  parts  of  the  circum- 
ference, it  ought  not  to  tend  to  fall  in  one  direction  rather  than  in 
any  other.  This  point  of  view,  not  easily  taken  by  the  layman, 
illustrates  the  natural  tendency  of  the  Greek  philosopher  to  em- 
phasize geometrical  symmetry. 

Among  those  who  say  that  the  first  principle  is  one  and  movable 
and  infinite  is  Anaximander  of  Miletos,  son  of  Praxiades,  pupil  and 
successor  of  Thales.  He  said  that  the  first  principle  and  element  of 
all  things  is  infinite,  and  he  was  the  first  to  apply  this  word  to  the 
first  principle ;  and  he  says  that  it  is  neither  water  nor  any  other  one 
of  the  things  called  elements,  but  the  infinite  is  something  of  a  dif- 
ferent nature  from  which  came  all  the  heavens  and  the  worlds  in 
them;  and  from  what  source  things  arise,  but  that  they  return  of 
necessity  when  they  are  destroyed.  .  .  .  Evidently  when  he  sees  the 
four  elements  changing  into  one  another,  he  does  not  deem  it  right  to 
make  any  one  of  these  the  underlying  substance,  but  something  else 
besides  them.  —  Theophrastus. 

The  earth  is  a  heavenly  body,  controlled  by  no  other  power  and 
keeping  its  position  because  it  is  the  same  distance  from  all  things. 
The  form  of  it  is  curved,  cylindrical,  like  a  stone  column.  It  has  two 
faces.  One  of  these  is  the  ground  beneath  our  feet  and  the  other  is 
opposite  to  it.  The  stars  are  the  circle  of  fire,  separated  from  the 
fire  about  the  world,  and  surrounded  by  air.  There  are  certain 
breathing-holes  like  the  holes  of  a  flute  through  which  we  see  the 
stars ;  so  that  when  the  holes  are  stopped  up  there  are  eclipses.  The 
moon  is  sometimes  full  and  sometimes  in  other  phases,  as  these  holes 
.are  stopped  up  or  open.  The  circle  of  the  sun  is  27  times  that  of  the 
moon.  .  .  .  Man  came  into  being  from  another  animal,  namely  the 
fish,  for  at  first  he  was  like  a  fish.  —  Hippolytus  (on  Anaximander). 


48  A  SHORT  HISTORY  OF  SCIENCE 

Anaximander,  collecting  data  from  the  Ionian  sailors  frequent- 
ing Miletus,  constructed  a  map  of  the  earth,  and  speculated  on  the 
relative  distances  of  the  heavenly  bodies. 

Herodotus  relates  that 

during  the  reign  of  Cleomenes,  Aristagoras,  prince  of  Miletus,  ar- 
rived at  Sparta;  the  Lacedaemonians  affirm,  that  desiring  to  have 
a  conference  with  their  sovereign,  he  appeared  before  him  with  a 
tablet  of  brass  in  his  hand,  on  which  was  inscribed  every  known  part 
of  the  habitable  world,  the  seas,  and  the  rivers. 

ANAXIMENES.  —  A  third  Ionian  Greek,  often  associated  with 
those  just  mentioned,  is  Anaximenes  (sixth  century  B.C.),  like  them 
a  native  of  Miletus.  For  him  the  stars  are  fixed  upon  the  celes- 
tial vault,  and  pass  behind  the  northern  (highest)  part  of  the  earth 
on  setting.  Air,  not  water,  is  the  first  cause  of  all  things,  the 
others  being  formed  by  its  compression  or  rarefaction.  The  heat 
of  the  sun  is  due  to  its  rapid  motion,  but  the  stars  are  too  remote 
to  give  out  heat. 

Anaximenes  arrived  at  the  conclusion  that  air  is  the  one  movable, 
infinite,  first  principle  of  all  things.  For  he  speaks  as  follows :  '  Air 
is  the  nearest  to  an  immaterial  thing ;  for  since  we  are  generated  in 
the  flow  of  air,  it  is  necessary  that  it  should  be  infinite  and  abundant, 
because  it  is  never  exhausted.'  (A  fragment  accredited  to  Anax- 
imenes.) 

Most  of  the  earlier  students  of  the  heavenly  bodies  believed  that 
the  sun  did  not  go  underneath  the  earth  but  rather  around  the  earth 
and  this  region,  and  that  it  disappeared  from  the  view  and  produced 
night  because  the  earth  was  so  high  toward  the  north.  .  .  .  Anaxim- 
enes and  Anaxagoras  and  Democritus  say  that  the  breadth  of  the 
earth  is  the  reason  why  it  remains  where  it  is.  .  .  .  Anaximenes  says 
that  the  earth  was  wet,  and  when  it  dried  it  broke  apart,  and  that 
earthquakes  are  due  to  the  breaking  and  falling  of  hills.  —  Aristotle. 

The  school  of  Thales  and  his  successors  in  this  Ionian  outpost 
of  Greek  civilization  was  soon  succeeded  by  developments  of  still 
greater  importance  in  the  more  remote  Italian  colonies. 


BEGINNINGS  IN  GREECE  49 

PYTHAGORAS  AND  HIS  SCHOOL.  —  The  register  of  mathemati- 
cians proceeds :  —  "After  these  Pythagoras  transformed  the  occu- 
pation with  this  branch  into  a  true  science,  by  considering  the 
foundation  of  it  from  a  higher  standpoint,  and  investigated  its 
theorems  in  a  more  abstract  and  intellectual  way.  It  is  he  also 
who  invented  the  theory  of  the  irrational  and  the  construction 
of  the  cosmical  bodies."  These  few  words  like  those  quoted  of 
Thales  are  full  of  meaning.  The  Egyptian  priests  knew 
geometrical  facts,  the  raw  material  of  mathematical  science; 
Thales  adapted  this  material  to  building  purposes,  Pythagoras 
began  the  systematic  foundations  of  the  structure.  Both  in 
name  and  in  substance  mathematics  as  a  science  begins  with 
Pythagoras. 

Pythagoras  founded  in  the  Greek  cities  of  southern  Italy  a 
school  which  had  much  of  the  character  of  a  fraternity  or  secret 
society,  this  with  political  tendencies  ultimately  arousing  hos- 
tility which  proved  destructive  to  it.  Beyond  these  undisputed 
facts  his  life  and  work  are  obscured  by  a  great  mass  of  tradition 
and  myth,  even  the  date  of  his  birth  being  doubtful.  A  native 
of  the  island  of  Samos  not  far  from  Miletus,  he  appears  to  have 
been  much  affected  by  Egyptian  influences  during  a  residence  in 
that  country.  A  visit  to  Babylon  even  is  alleged,  but  with  doubt- 
ful authority.  The  etiquette  of  the  Pythagorean  school  required 
that  all  discoveries  should  be  attributed  to  the  "Master"  and 
not  revealed  to  outsiders.  To  Pythagoras  himself  must  probably 
be  ascribed  the  so-called  Pythagorean  theorem,  this  forming  the 
necessary  basis  for  the  theory  of  the  irrational  mentioned  in  the 
register.  A  similar  inference  may  be  drawn  in  regard  to  the  reg- 
ular polyhedra.  On  the  other  hand,  Pythagoras  appears  to  have 
interested  himself  in  the  theory  of  numbers,  particularly  in  con- 
nection with  music  and  geometry.  He  is  said  to  have  first  in- 
troduced weights  and  measures  among  the  Greeks. 

The  attribution  of  particular  results  or  beliefs  to  individuals  of 
this  period  is  however  very  doubtful  on  account  of  the  fact  that 
Pythagoras  left  no  writings  whatever,  that  his  school  was  es- 
sentially a  secret  society,  and  that  in  later  centuries  it  became 


50  A  SHORT  HISTORY  OF  SCIENCE 

the  custom  to  credit  its  founder  with  all  sorts  of  knowledge  which 
he  could  not  possibly  have  possessed. 

Pythagoras  makes  the  classification,  arithmetic  (numbers 
absolute),  music  (numbers  applied),  geometry  (magnitudes  at 
rest),  astronomy  (magnitudes  in  motion),  this  fourfold  division  or 
"  quadrivium  "  continuing  in  vogue  for  some  two  thousand  years. 
The  distinction  between  abstract  and  concrete  arithmetic  had  been 
emphasized  among  the  Greeks  in  comparatively  early  times. 
Arithmetic  and  geometry  were  distinguished  on  one  side  from 
mechanics,  astronomy,  optics,  surveying,  music,  and  computation 
on  the  other.  The  aim  of  Greek  arithmetic  "was  entirely  differ- 
ent from  that  of  the  ordinary  calculator,  and  it  was  natural  that 
the  philosopher  who  sought  in  numbers  to  find  the  plan  on  which 
the  Creator  worked,  should  begin  to  regard  with  contempt  the 
merchant  who  wanted  only  to  know  how  many  sardines,  at  10  for 
an  obol,  he  could  buy  for  a  talent." 

The  limited  mathematics  of  the  practical  Egyptians  had  con- 
sisted of  numerical  cases.  It  was  an  easy  step  for  Pythagoras  to 
make  number  in  a  somewhat  mystical  sense  the  central  element 
in  his  philosophy. 

PYTHAGOREAN  ARITHMETIC.  —  In  pure  arithmetic  or  number 
theory  as  we  should  call  it,  the  Pythagoreans  enunciated  such 
dicta  as,  for  example,  "Unity  is  the  origin  and  beginning  of  all 
numbers  but  not  itself  a  number."  Prime  and  composite  num- 
bers were  also  distinguished,  and  theorems  of  considerable  alge- 
braic complexity  discovered.  There  is  naturally  no  algebraic 
symbolism,  but  "unknown"  and  "given"  quantities  are  employed 
in  the  modern  sense.  Odd  and  even  numbers  received  special 
names,  and  besides  the  series  of  squares  and  cubes  and  the  arith- 
.  metic  and  geometric  progressions  previously  known, 

•    •  other  series  were  derived  from  these,  for  example, 

•    •    •         the  triangular  numbers :   1,  3,  6,  10,  15,  etc.,  by 

*    *       successive  addition  of  the  natural  numbers.     The 

reason  for  the  name  triangular  will  be  clear  if  one 

counts  the  dots  in  the  triangle  formed  by  taking  one,  two,  three  or 

more  rows  beginning  at  the  top  of  the  figure. 


11 


BEGINNINGS  IN  GREECE  51 

The  series  of  squares  is  formed  by  adding  the  odd  numbers 
successively;  1+3  =  4,  1+3+5  =  9,  etc.  The  series  2,  6, 
12,  20,  30,  etc.  is  formed  by  adding  the  even 
numbers,  or  again  by  multiplying  adjacent 
natural  numbers.  If  we  construct  a  series  of 
squares  or  parallelograms  with  a  common  angle 
and  sides  of  length  1,  2,  3,  4,  5,  etc.  the  figure 
which  must  be  added  to  any  one  to  produce 
the  next  larger  was  called  by  the  Greeks  a 
gnomon,  the  area  of  which  would  be  repre- 
sented by  one  of  the  series  of  odd  numbers,  —  an  interesting  and 
typical  example  of  the  Greek  habit  of  combining  geometry  with 
number-theory.  As  products  of  two  numbers  were  associated  with 
areas  —  "square"  or  "oblong"  —  so  products  of  three  factors 
were  interpreted  as  volumes.  A  later  Pythagorean  calls  the  cube 
the  "  geometrical  harmony  "  —  an  expression  embodying  the  as- 
sociation of  mathematics  with  music.  The  cube  has  indeed  6 
faces,  8  vertices,  12  edges ;  6,  8,  and  12  are  in  harmonic  progres- 
sion, that  is,  8  is  the  harmonic  mean  between  6  and  12. 
->  PYTHAGOREAN  GEOMETRY.  —  In  geometry  the  Pythagoreans 
formulated  definitions  of  the  fundamental  elements,  line,  sur- 
face, angle,  etc.  They  are  credited  with  a  number  of  theorems 
depending  on  the  application  of  one  surface  to  another,1  and  im- 
plying a  knowledge  of  methods  of  determining  area  and  of  the 
properties  of  parallel  lines.  They  developed  a  fairly  complete 
theory  of  the  triangle,  including  the  fundamental  proof  that  the 
sum  of  the  angles  of  a  triangle  is  two  right  angles,  by  a  method 
not  very  different  from  our  own.  The  theory  of  the  "cosmical 
bodies"  mentioned  in  the  register  is  of  special  in- 
/  \  /  \  terest.  Any  solid  angle  must  have  at  least  three 

y^- ^    faces.     If  three  equal  equilateral  triangles  have  a 

/    \        common   vertex  they  will  when  cut  or  folded    so 
that  their  edges  are  brought  together,  form  a  solid 
angle,  and  a  fourth  equal   triangle  will  complete  a  regular  tet- 
rahedron.    Similarly,    if  we  start  with  four   triangles,  we  may 

1  Some  of  these  are  equivalent  to  the  solution  of  the  quadratic  equation. 


52  A  SHORT  HISTORY  OF  SCIENCE 

build  up  with  four  others  a  regular  octahedron,  or  starting  with  five, 
an  icosahedron  with  20  faces.  Six  triangles,  however,  will  fill  the 
angular  space  about  a  point,  and  thus  not  permit  the  formation  of 
a  regular  polyhedron.  Using  squares  instead  of  triangles,  we 
obtain  only  the  cube ;  using  pentagons  (angle  108°),  the  regular 
dodecahedron  —  12  faces,  3  at  each  vertex.  The  Egyptians  must 
have  been  familiar  with  the  cube,  the  regular  tetrahedron,  and  the 
octahedron.  To  these,  with  the  icosahedron,  the  Pythagoreans  as- 
sociated the  four  cosmical  elements  —  earth,  air,  fire,  and  water. 
Their  discovery  of  an  additional  body,  the  regular  dodecahedron, 
formed  by  12  pentagons,  made  a  break  in  the  correspondence,  and 
the  need  was  met  by  the  addition  of  the  universe,  or,  according 
to  others,  the  ether,  as  a  fifth  term  in  the  cosmical  series.  This 
correspondence  was  not  merely  symbolical,  but  physical,  the 
earth  being  supposed  to  consist  of  cubical  particles,  etc.  We 
cannot  infer  that  the  impossibility  of  a  sixth  regular  polyhedron 
was  known.  That  only  these  five  regular  polyhedra  are  pos- 
sible was  in  fact  first  proved  by  Euclid.  There  is  a  tradition 
that  the  Pythagorean  discoverer  of  the  dodecahedron  was 
drowned  at  sea  on  account  of  the  sacrilege  of  announcing  his 
discovery  publicly.  A  later  commentator  records  a  similar 
tradition  that  the  discoverer  of  the  irrational  perished  by 
shipwreck,  since  the  inexpressible  should  remain  forever  con- 
cealed, and  that  he  who  touched  and  opened  up  this  picture 
of  life  was  transported  to  the  place  of  creation  and  there  washed 
in  eternal  floods. 

The  regular  polygons  were  naturally  studied,  and  in  particu- 
lar the  decomposition  of  them  into  right  triangles  of  45°  and 
30°-60°.  With  the  pentagon  the  attempt  naturally  failed,  but 
the  five-pointed  star  formed  by  drawing  diagonals  was  a  special 
emblem  of  the  Pythagoreans.  With  the  inscribed  pentagon 
connects  itself  naturally  the  division  of  a  line  in  extreme  and 
mean  ratio,  or,  as  it  was  later  characterized,  the  "golden  sec- 
tion." This  division,  by  which  the  square  on  the  greater  segment 
of  a  line  is  equivalent  to  the  rectangle  whose  sides  are  the  other 
segment  and  the  whole  line,  occurs  repeatedly  in  Greek  archi- 


BEGINNINGS  IN  GREECE  53 

tecture  of  the  fifth  century,  with  fine  effect,  and  must  have  been 
systematically  employed. 

As  to  the  celebrated  theorem  which  bears  the  name  of  Pythag- 
oras, he  may  well  have  learned  from  the  Egyptian  rope-stretchers 
that  a  right  angle  is  formed  by  taking  sides  of  lengths  3  and  4  and 
separating  the  other  ends  a  distance  5,  while  his  study  of  numbers 
would  easily  have  led  to  the  discovery  that  in  the  series  of  squares 
the  adjacent  9  and  16  make  25.  It  would  naturally  be  investi- 
gated whether  a  similar  relation  could  be  verified  for  other  right 
triangles.  In  the  most  familiar  case  of  the  isosceles  right  tri- 
angle it  soon  appears  that  the  length  of  the  equal  sides  being  taken 
as  1,  the  length  of  the  hypotenuse  could  be  only  approximately 
expressed.  It  cannot  indeed  be  exactly  expressed  by  any  whole 
number,  or  fraction;  it  is  irrational. 

If  it  is  true  as  Whewell  says,  that  the  essence  of  the  triumphs  of 
science  and  its  progress  consists  in  that  it  enables  us  to  consider  evident 
and  necessary,  views  which  our  ancestors  held  to  be  unintelligible  and 
were  unable  to  comprehend,  then  the  extension  of  the  number  concept 
to  include  the  irrational,  and  we  will  at  once  add,  the  imaginary, 
is  the  greatest  forward  step  which  pure  mathematics  has  ever  taken. 

—  Hankel 

In  this  case  the  proof  of  the  Pythagorean  theorem  is  easily 
effected  by  a  simple  graphical  construction,  involving  merely  the 
drawing  of  diagonals  of  squares.  The  smaller 
triangles  in  the  figure  are  evidently  all  equal. 
The  larger  square  contains  four  of  them,  the 
smaller  squares,  two  each.  It  seems  possible 
that  this  was  the  Pythagorean  method,  but  as 
to  how  the  proof  was  accomplished  in  other  cases 
we  have  no  information,  the  simpler  proof  of  Euclid  having  com- 
pletely superseded  the  earlier.  On  the  other  hand,  for  the  cor- 
responding arithmetical  problem  of  finding  three  whole  numbers 
which  can  be  the  sides  of  a  right  triangle,  Pythagoras  is  said  to 
have  given  a  correct  solution,  equivalent  in  our  notation  to 

(2  a  +  I)2  +  (2a2  +  2a)2  =  (2a2  +  2a  +  I)2, 


54  A  SHORT  HISTORY  OF  SCIENCE 

a  denoting  any  positive  integer.  How  this  method  was  discovered 
remains  a  matter  of  conjecture. 

We  may  recognize  here  the  characteristic  elements  of  the  in- 
ductive method,  first,  observation  of  the  particular  fact  that  in  a 
certain  right  triangle,  with  sides  3,  4,  and  5,  the  sum  of  the  squares 
on  the  two  sides  is  equal  to  that  on  the  hypotenuse ;  second,  the 
formation  of  the  hypothesis  that  this  may  be  true  also  for  right 
triangles  in  general;  third,  the  verification  of  the  hypothesis  in 
other  particular  cases.  Then  follows  the  deductive  confirmation 
of  the  hypothesis  as  a  law  for  all  right  triangles. 

PYTHAGOREAN  PHYSICAL  SCIENCE.  —  It  has  been  already  noted 
that  one  of  the  most  fundamental  principles  of  the  Pythagorean 
school  was  the  significance  attached  to  number  in  connection 
with  all  sorts  of  phenomena,  the  regular  motions  of  the  heavenly 
bodies,  the  musical  tones,  etc.  There  is  a  tradition  that  Pythag- 
oras, walking  one  day,  meditating  on  the  means  of  measuring 
musical  notes,  happened  to  pass  near  a  blacksmith's  shop,  and 
had  his  attention  arrested  by  hearing  the  hammers  as  they  struck 
the  anvil  produce  sounds  which  had  a  musical  relation  to  each 
other.  It  was  found  that  vibrating  cords  emitted  tones  de- 
pendent in  a  simple  way  on  their  length;  for  example,  cords  of 
lengths  2,  3,  and  4  giving  a  tone,  its  fifth  and  its  octave  re- 
spectively. The  monochord  used  in  studying  these  numerical 
relations  is  said  to  have  been  the  first  apparatus  of  experimental 
physics.  It  was  even  supposed  that  each  of  the  various 
heavenly  bodies  and  the  sphere  of  the  fixed  stars  had  a  char- 
acteristic tone,  these  all  uniting  to  produce  the  so-called  "  music 
of  the  spheres." 

TERRESTRIAL  MOTION  ;  PHILOLAUS,  HICETAS.  —  The  universe 
was  believed  to  consist  of  the  four  elements,  —  earth,  air,  fire,  water, 
—  to  be  a  sphere  with  a  spherical  earth  at  its  centre,  and  to  have 
life.  Pythagoras  identified  the  morning  and  evening  stars,  and 
attributed  the  moon's  light  to  reflection.  It  is  of  peculiar  interest 
that  later  Pythagoreans,  in  particular  Philolaus,  about  400  B.C., 
attributed  the  apparent  daily  motion  of  the  heavenly  bodies  from 
east  to  west  not  to  their  own  actual  motion  but  to  a  motion  of 


BEGINNINGS  IN  GREECE  55 

the  earth  in  the  opposite  direction.  This  latter  motion,  however, 
was  thought  of,  not  as  a  rotation,  but  as  an  orbital  motion  about  a 
so-called  "central  fire."  Just  as  the  moon  revolved  about  the 
earth,  always  turning  the  same  face  towards  the  latter,  so  the 
earth  might  revolve  about  the  central  fire  which  would  be  forever 
invisible  to  the  inhabitants  of  the  other  side  of  the  earth.  While 
we  say  that  the  moon  rotates  about  its  axis  in  the  same  time  in 
which  it  revolves  about  the  earth,  to  the  ancients  such  a  motion 
was  not  considered  to  include  rotation  at  all.  A  further  essen- 
tially arbitrary  assumption  introduced  between  the  earth  and 
the  central  fire  a  counter-earth  (antichthori) ,  which  was  required  to 
make  up  the  supposed  number  of  the  heavenly  bodies,  and  which 
would  hide  the  central  fire  from  dwellers  in  the  antipodes. 
Aristotle,  criticising  this  theory,  says  of  the  Pythagoreans :  — 

They  do  not  with  regard  to  the  phenomena  seek  for  their  reasons 
and  causes,  but  forcibly  make  the  phenomena  fit  their  opinions  and 
preconceived  notions.  .  .  .  When  they  anywhere  find  a  gap  in  the 
numerical  ratios  of  things,  they  fill  it  up  in  order  to  complete  the  sys- 
tem. As  ten  is  a  perfect  number  and  is  supposed  to  comprise  the 
whole  nature  of  numbers,  they  maintain  that  there  must  be  ten  bodies 
moving  in  the  universe,  and  as  only  nine  are  visible,  they  make  the 
antichthon  the  tenth. 

All  the  other  heavenly  bodies  describe  orbits,  each  in  its  own 
hollow  sphere  about  the  central  fire,  the  generally  adopted  order, 
based  on  the  apparent  rate  of  motion  among  the  stars,  being 
Moon,  Sun,  Venus,  Mercury,  Mars,  Jupiter,  Saturn.  Pythagorean 
speculations  as  to  relative  distances  of  the  different  planets  were 
naturally  mystical  notions  merely.  The  sun  was  said  to  move 
around  the  central  fire  in  an  "oblique  circle,"  i.e.  the  ecliptic. 
The  moon  was  believed  to  be  inhabited  by  plants  and  animals. 
The  moon  might  be  eclipsed  either  by  the  earth  or  by  the 
counter-earth.  This  remarkable  system,  admitting  the  earth  to 
move  and  not  to  be  the  centre  of  the  universe,  was  not  generally 
or  long  accepted,  but  had  a  share  in  securing  the  acceptance  of 
the  theories  of  Copernicus  nearly  2000  years  later.  One  at  least 


56  A  SHORT  HISTORY  OF  SCIENCE 

of  the  Pythagoreans  made  the  great  further  step,  somewhat  loosely 
described  by  Cicero  in  the  words :  — 

Hicetas  of  Syracuse,  according  to  Theophrastus,  believes  that  the 
heavens,  the  sun,  moon,  stars,  and  all  heavenly  bodies  are  standing 
still,  and  that  nothing  in  the  universe  is  moving  except  the  earth, 
which,  while  it  turns  and  twists  itself  with  the  greatest  velocity  round 
its  axis,  produces  all  the  same  phenomena  as  if  the  heavens  were  moved 
and  the  earth  were  standing  still. 

The  activity  of  the  Pythagorean  school  continued  to  be  im- 
portant until  about  400  B.C.,  that  is,  until  the  rise  of  the  Athenian 
school  under  Plato  and  his  successors.  It  had  not  only  created 
the  science  of  mathematics ;  it  had  developed,  however  vaguely 
and  imperfectly,  the  idea  of  a  world  of  physical  phenomena 
governed  by  mathematical  laws. 

Dr.  Allman  says  of  Pythagoras :  — 

In  establishing  the  existence  of  the  regular  solids  he  showed 
his  deductive  power;  in  investigating  the  elementary  laws  of 
sound  he  proved  his  capacity  for  induction;  and  in  combining 
arithmetic  with  geometry  ...  he  gave  an  instance  of  his  philosophic 
power. 

These  services,  though  great,  do  not  form,  however,  the  chief  title  of 
the  Sage  to  the  gratitude  of  mankind.  He  resolved  that  the  knowl- 
edge which  he  had  acquired  with  so  great  labour,  and  the  doctrine 
which  he  had  taken  such  pains  to  elaborate,  should  not  be  lost; 
and  .  .  .  devoted  himself  to  the  formation  of  a  society  d' elite,  which 
would  be  fit  for  the  reception  and  transmission  of  his  science  and 
philosophy ;  and  thus  became  one  of  the  chief  benefactors  of  human- 
ity, and  earned  the  gratitude  of  countless  generations. 

In  medicine,  we  meet  before  the  fifth  century  only  with  the 
anatomist  Alcmaeon  (508  B.C.)  of  the  early  medical  school  at 
Crotona,  in  Italy,  and  in  natural  philosophy  (besides  Thales  and 
others  already  mentioned)  with  Xenophanes,  who,  like  Pythagoras, 
held  that  fossils  are  in  fact  what  they  appear  to  be,  and  not  mere 
"  freaks  of  nature,"  as  was  generally  believed. 


BEGINNINGS  IN  GREECE 


57 


REFERENCES  FOR  READING 

ALLMAN.     Greek  Geometry.    Chapters  I,  II. 

BALL.     A  Short  History  of  Mathematics.     Chapter  II. 

BERRY.     A  History  of  Astronomy.    Chapter  II  to  page  26. 

CAJORI.     A  History  of  Mathematics.    Pages  16-23. 

DREYER.    Planetary  Systems.     Chapters  I,  II. 

GOMPERZ.     Greek  Thinkers.     Vol.  I,  pp.  1-164. 

Gow.    History  of  Greek  Mathematics.    Chapters  III,  IV,  VI. 

HEATH.    Aristarchus  of  Samos. 

BUTCHER.     Aspects  of  the  Greek  Genius. 


MAP  OF  THE  WORLD  ACCORDING  TO  HERODOTUS 
(From  Breasted's  Ancient  Times.    Courtesy  of  Messrs.  Ginn  &  Co.) 

From  long  journeys  in  Egypt  and  other  Eastern  Countries  Herodotus  returned  with  much 
information  regarding  these  lands.  His  map  showed  that  the  Red  Sea  connected  with  the 
Indian  Ocean,  a  fact  unknown  to  his  predecessor,  Hecataeua.  [See  p.  34.] 

—  Breasted. 


CHAPTER  IV 
SCIENCE  IN  THE  GOLDEN  AGE  OF  GREECE 

Our  science,  in  contrast  with  others,  is  not  founded  on  a  single 
period  of  human  history,  but  has  accompanied  the  development  of 
culture  through  all  its  stages.  Mathematics  is  as  much  interwoven 
with  Greek  culture  as  with  the  most  modern  problems  in  engineer- 
ing. She  not  only  lends  a  hand  to  the  progressive  natural  sciences,  but 
participates  at  the  same  time  in  the  abstract  investigations  of  logicians 
and  philosophers.  —  Klein. 

There  still  remain  three  studies  suitable  for  freemen.  Calcu- 
lation in  arithmetic  is  one  of  them;  the  measurement  of  length, 
surface,  and  depth  is  the  second ;  and  the  third  has  to  do  with  the 
revolutions  of  the  stars  in  reference  to  one  another  .  .  .  there  is  in 
them  something  that  is  necessary  and  cannot  be  set  aside  ...  if 
I  am  not  mistaken,  [something  of]  divine  necessity.  —  Plato. 

LITERATURE  AND  ART.  —  The  fifth  century  B.C.  witnessed  that 
astonishing  flowering  of  the  Greek  genius  in  literature  and  mili- 
tary glory  which  has  made  it  ever  since  famous.  The  battles 
of  Marathon  and  Salamis  had  flung  back  the  Asiatic  hosts  which 
threatened  to  overrun  and  enslave  Europe,  and  had  transformed 
the  Greeks  from  a  group  of  jealous  and  parochial  city  states  into 
a  great  democratic  nation.  Trade  prospered,  wealth  increased, 
and  for  about  a  century  letters,  art,  and  science  flourished  as  never 
before  and  never  since.  History  began  to  be  written  by  Herodotus 
and  Thucydides.  The  drama  was  developed  by  ^Eschylus, 
Sophocles,  and  Euripides  to  such  a  pitch  that  even  to-day,  after 
the  lapse  of  nearly  2500  years,  crowds  listen  with  eager  interest 
to  the  (Edipus  of  Sophocles  and  the  Iphigenia  of  Euripides,  while 
the  poetry  of  Pindar  and  the  wit  of  Aristophanes  have  never  lost 
their  charm.  In  architecture  and  the  plastic  arts  the  Parthenon 
and  its  sculptures  still  testify  to  Greek  supremacy.  - 

58 


THE  GOLDEN  AGE  OF  GREECE         59 

In  science,  also,  great  names  testify  to  memorable  deeds.  No 
such  perfection,  to  be  sure,  was  attained  in  science  as  in  literature 
and  in  sculpture,  but  vast  progress  was  made  in  mathematical 
science  beyond  anything  hitherto  accomplished,  and  the  founda- 
tions were  securely  laid  for  a  rational  interpretation  of  man  and 
of  nature.  Literature,  architecture,  sculpture,  and  the  drama  re- 
quire no  special  apparatus  or  reagents.  Mathematical  science  also 
is  not  dependent  upon  such  externals,  being  in  this  respect  like 
literature  and  art,  and  we  find  geometry  and  arithmetic  at  the 
outset  moving  forward  far  more  rapidly  than  natural  or  physi- 
cal science. 

PARMENIDES.  —  The  recognition  of  the  spherical  shape  of  the 
earth  and  its-  division  into  zones  are  attributed  not  only  to  the 
Pythagoreans,  but  also  to  Parmenides  of  Elis,  who  lived  in  the 
early  part  of  the  fifth  century.  He  introduced  a  system  of  concen- 
tric spheres  analogous  to  that  soon  to  be  so  highly  developed 
by  Eudoxus.  He  identified  the  evening  and  the  morning  stars, 
and  attributed  the  moon's  brightness  to  reflected  light.  He 
regarded  the  sun  as  consisting  of  hot  and  subtle  matter  detached 
from  the  Milky  Way,  the  moon  chiefly  of  the  dark  and  cold. 

EMPEDOCLES.  —  Passing  over  the  guesses  of  Heraclitus  and 
Parmenides  at  the  riddle  of  existence  and  of  man  and  nature,  we 
may  pause  for  a  moment  to  examine  the  speculations  of  Empedocles 
(about  455  B.C.).  A  native  of  Agrigentum  in  southern  Sicily, 
Empedocles  was  regarded  as  poet,  philosopher,  seer,  and  im- 
mortal god.  He  appears  to  have  been  a  close  observer  of  nature, 
understanding  the  true  cause  of  solar  eclipses  and  believing  the 
moon  to  be  twice  as  far  from  the  sun  as  from  the  earth.  The 
latter  is  held  in  place  by  the  rapidly  rotating  heavens  "as  the 
water  remains  in  a  goblet  which  is  swung  quickly  round  in  a 
circle."  Aristotle  attributes  to  Empedocles  that  analysis  of  the 
universe  into  the  four  "elements/'  earth,  air,  fire,  and  water,  which 
until  comparatively  recent  times  was  universally  accepted  as 
fundamental.  It  is,  nevertheless,  not  only  misleading  but  absurd 
to  hold  with  Gomperz  ("Greek  Thinkers,"  I,  230)  that  Em- 
pedocles' theory  of  the  four  elements  "takes  us  at  a  bound  into 


60  A    SHORT    HISTORY    OF   SCIENCE 

the  heart  of  modern  chemistry."  The  facts  seem  rather  to  be 
that  Empedocles  put  together  and  hospitably  accepted  and 
clarified  the  theories  of  his  various  predecessors.  He  is  the 
first  sanitarian  of  whom  we  have  any  record,  for  Empedocles 
is  credited  with  having  cut  down  a  hill  of  his  native  city  and 
thus  cured  a  plague  by  letting  in  the  north  wind,  and  to  have 
done  a  similar  service  to  the  neighboring  "parsley"  city  of  Selinus 
(Selinunte)  by  simply  draining  a  local  marsh. 
The  following  is  a  fragment  from  the  writings  of  Empedocles :  — 

So  all  beings  breathe  in  and  out;  all  have  bloodless  tubes  of 
flesh  spread  over  the  outside  of  the  body,  and  at  the  openings  of  these 
the  outer  layers  of  skin  are  pierced  all  over  with  close-set  ducts,  so 
that  the  blood  remains  within,  while  a  facile  opening  is  cut  for  the  air 
to  pass  through.  Then  whenever  the  soft  blood  speeds  away  from 
these,  the  air  speeds  bubbling  in  with  impetuous  wave,  and  when- 
ever the  blood  leaps  back  the  air  is  breathed  out;  as  when  a  girl, 
playing  with  a  clepsydra  of  shining  brass,  takes  in  her  fair  hand  the 
narrow  opening  of  the  tube  and  dips  it  in  the  soft  mass  of  silvery 
water,  the  water  does  not  at  once  flow  into  the  vessel,  but  the  body  of 
air  within  pressing  on  the  close-set  holes  checks  it  till  she  uncovers 
the  compressed  stream;  but  then  when  the  air  gives  way  the  de- 
termined amount  of  water  enters.  And  so  in  the  same  way  when  the 
water  occupies  the  depths  of  the  bronze  vessel,  as  long  as  the  narrow 
opening  and  passage  is  blocked  up  by  human  flesh,  the  air  outside, 
striving  eagerly  to  enter,*holds  back  the  water  inside  behind  the  gates 
of  the  resounding  tube,  keeping  control  of  its  end,  until  she  lets  go 
with  her  hand.  Then,  on  the  other  hand,  the  very  opposite  takes 
place  to  what  happened  before;  the  determined  amount  of  water 
runs  off  as  the  air  enters.  Thus  in  the  same  way  when  the  soft  blood, 
surging  violently  through  the  members,  rushes  back  into  the  interior, 
a  swift  stream  of  air  comes  in  with  hurrying  wave,  and  whenever  it 
[the  blood]  leaps  back,  the  air  is  breathed  out  again  in  equal  quantity. 

—  Fairbanks. 

ANAXAGORAS.  —  (500-428  B.C.)  For  the  student  of  science 
Anaxagoras,  a  native  of  Clazomene  in  Asia  Minor,  is  more  im- 
portant than  Empedocles.  Turning  aside  from  wealth  and  civic 
distinction  in  his  enthusiasm  for  science,  he  seems  to  have  occupied 


THE  GOLDEN  AGE  OF  GREECE         61 

himself  with  the  problem  of  squaring  the  circle,  a  problem  at- 
tacked even  by  the  Egyptians  with  some  degree  of  success,  and 
destined  to  exercise  great  influence  on  the  development  of  Greek 
geometry.  The  beginnings  of  perspective  are  also  attributed  to 
him,  in  connection  with  studies  of  the  stage.  He  was  particu- 
larly interested  in  a  great  meteorite  —  the  appearance  of  which 
he  was  afterwards  said  to  have  predicted  —  supposing  it  to  have 
fallen  from  the  sun,  and  inferring  that  the  latter  was  a  "  mass  of 
red-hot  iron  greater  than  the  Peloponnesus,"  not  very  distant 
from  the  earth.  Like  the  Pythagoreans  he  assigned  as  the 
order  of  distances :  —  moon,  sun,  Venus,  Mercury,  Mars,  Jupiter, 
Saturn.  The  earth's  axis  was  inclined,  in  order  that  there 
might  be  variations  of  climate  and  habitability.  He  explained 
the  moon's  phases  correctly,  also  solar  and  lunar  eclipses,  but 
he  misinterpreted  the  Milky  Way  as  due  to  the  shadow  cast 
by  the  earth.  His  theory  of  the  nature  and  origin  of  the  cosmos, 
viz.  that  it  was  material  and  had  come  by  the  combination  and 
differentiation  of  primitive  elementary  substances  or  "seeds"  of 
matter,  was  repugnant  to  those  holding  the  polytheistic  dogmas 
of  his  time  and  brought  him  into  popular  disfavor.  Convicted 
of  impiety,  he  died  in  exile,  428  B.C.  By  his  insistence  upon  the 
importance  of  minute  invisible  "seeds"  or  particles  of  matter  he 
paved  the  way  for  the  "atomism"  of  Leucippus  and  Democritus. 
THE  ATOMISTS.  —  A  very  little  observation  of  external  nature 
shows  that  disintegration  is  forever  going  on.  Ice  turns  to  water, 
water  to  vapor,  rocks  to  sand  and  sand  to  dust  —  in  other  words, 
masses  to  particles.  Furthermore,  dust  vanishes  and  vapor  dis- 
appears, while  clouds  and  fogs,  rain  and  snow,  make  their  appear- 
ance without  obvious  cause,  and  dust  accumulates  from  invisible 
sources.  What  is  more  reasonable  than  to  suppose  that  visible 
things  —  rocks  and  ice  and  water  —  become  gradually  resolved  into 
invisible  particles,  and  that  these  in  their  turn  condense  into  new 
visible  substances  at  some  later  time?  For  these  or  similar 
ideas  the  material  "seeds"  of  Anaxagoras  had,  as  stated  above, 
paved  the  way,  when  later  emphasized  by  Leucippus  and  his 
more  famous  pupil  Democritus.  Of  the  life  of  Leucippus 


62  A  SHORT  HISTORY  OF  SCIENCE 

almost  nothing  is  known,  but  he  was  probably  a  contem- 
porary of  Empedocles  and  Anaxagoras,  and  possibly  a  pupil 
of  Zeno.  Leucippus  assumed  the  existence  of  empty  space  as 
well  as  of  matter,  and  held  that  of  atoms  all  things  are  consti- 
tuted. Space  is  infinite  in  magnitude,  atoms  infinite  in  number 
and  indivisible,  with  only  quantitative  differences.  Atoms  are 
always  in  activity,  and  worlds  are  produced  by  atoms  variously 
shaped  and  weighted,  falling  in  empty  space  and  giving  rise  to  an 
eddying  motion  by  mutual  impact. 

DEMOCRITUS  OF  ABDERA  was  a  pupil  and  associate  of  Leu- 
cippus, whose  theories  of  empty  space  and  material  atoms  he  de- 
veloped and  made  so  famous  that  his  own  name  alone  is  often 
associated  with  them.  Of  his  life,  his  works,  and  his  death  little 
is  certainly  known,  but  he  may  be  regarded  as  marking  the  culmina- 
tion and  conclusion  of  the  Ionian  school ;  and  his  reputation,  both 
in  antiquity  and  in  mediaeval  times,  was  immense.  Like  contem- 
porary and  preceding  philosophers,  his  writings  were  in  verse,  and 
Cicero  is  said  to  have  deemed  his  style  worthy  of  comparison  with 
that  of  Plato.  His  somewhat  boastful  comparison  of  his  own 
geometrical  power  with  that  of  the  Egyptian  rope-stretchers  has 
been  quoted. 

Democritus  appears  to  have  agreed  closely  in  his  interpretation 
of  nature  with  Leucippus,  and  regarded  empty  space  and  atoms 
as  cosmic  elements.  He  also  held  that  by  the  motion  of  the  atoms 
was  produced  the  world  with  all  that  it  contains.  Soul  and  fire 
are  of  one  nature,  their  atoms  small,  smooth,  and  round.  By 
inhaling  them  life  is  maintained.  Hence  the  soul  perishes  with 
and  in  the  same  sense  as  the  body,  —  a  doctrine  which  made 
Democritus  odious  to  later  generations.  Dante,  for  example, 
places  him  far  down  in  hell  as  "ascribing  the  world  to  chance." 

The  atomic  theory  of  perception  held  that  from  every  object 
"images"  of  that  object  are  being  given  off  in  all  directions,  some 
of  which  enter  the  organs  of  sense  and  cause  "sensations."  De- 
mocritus further  held  that  sensations  are  the  only  sources  of  our 
knowledge.  He  was  regarded  as  one  of  the  extreme  sceptics  of 
antiquity,  as  e.g.  in  this  saying,  "  We  know  nothing :  not  even 


THE  GOLDEN  AGE  OF  GREECE         63 

if  there  is  anything  to  know."  Galileo,  himself  of  a  highly  scepti- 
cal turn  of  mind,  refers  with  approval  to  Democritus,  and  it  is 
probably  on  this  side,  i.e.  by  exemplification  of  the  critical  spirit, 
that  Democritus  rendered  his  greatest  service.  His  positive  con- 
tributions to  science,  even  in  atomism,  were  apparently  neither 
novel  nor  important.  Democritus  explained  the  Milky  Way 
as  composed  of  a  vast  number  of  small  stars,  but  to  his  dis- 
ciple, Metrodorus  of  Chios,  it  was  a  former  path  of  the  Sun. 

THE  BEGINNINGS  OF  RATIONAL  MEDICINE.  HIPPOCRATES  OF 
Cos.  —  Before  the  middle  of  the  fifth  century  B.C.,  science  in 
the  healing  art  had  no  existence.  Excepting  among  a  few  of  the 
more  enlightened,  sacrifices  and  other  appeals  to  the  gods  still 
characterized  medicine  as  a  priestly  rather  than  a  scientific  pro- 
fession, while  the  prevailing  ignorance  of  anatomy  and  physiology 
made  rational  treatment  of  the  sick  difficult  if  not  impossible. 
Alcmaeon,  in  the  previous  century,  had  taken  some  steps  in  the 
right  direction,  proving  for  example  that  the  sperm  does  not 
originate,  as  was  currently  believed,  in  the  spinal  marrow,  and  that 
the  brain  is  the  organ  of  mind,  and  advancing  a  naturalistic  theory 
of  disease  which  seems  to  foreshadow  that  of  his  great  successor 
Hippocrates. 

Two  island  centres  of  medical  lore  (they  can  hardly  be  called 
medical  schools),  both  of  the  cult  of  Asclepias,  existed  in  the 
southeastern  ^Egean,  viz.  Cos  and  Cnidus,  and  on  the  former  was 
born,  in  460  B.C.,  Hippocrates,  "the  Father  of  Medicine,"  in  the 
next  century  already  characterized  by  Aristotle  as  "the  Great." 
Of  his  life,  education,  practice,  and  writings  comparatively  little  is 
certainly  known.  Many  of  the  writings  attributed  to  him  are  of 
doubtful  authenticity  and  are  more  safely  assigned  to  the  Hip- 
pocratic  "school."  Enough  remain,  however,  especially  when 
added  to  the  references  by  later  authors  to  him  and  to  his  sayings 
and  to  his  methods  of  practice,  to  make  it  clear  that  in  every  re- 
spect Hippocrates  was  worthy  of  the  lofty  reputation  with  which 
his  name  has  come  down  to  us  after  five  and  twenty  centuries. 

And  yet  it  is  not  for  the  practical  arts  of  medicine  or  any  of  its 
basic  sciences  that  Hippocrates  did  his  most  famous  work.  It 


64  A  SHORT  HISTORY  OF  SCIENCE 

was  rather  in  his  attitude  toward  health  and  disease  that  his 
real  greatness  lay.  For,  as  far  as  we  know,  it  was  Hippocrates 
who  first  insisted  on  regarding  disease  as  a  natural  rather  than  a 
supernatural  process,  and  Hippocrates  who  first  urged  that  care- 
ful observation  and  study  of  the  patient  which  entitles  him  to 
rank  as  the  original  "clinician"  of  medical  science.  Again,  it 
was  Hippocrates  who  first  insisted  on  the  existence  and  importance 
of  those  processes  of  self-repair  which  are  to-day  recognized  as 
fundamental  properties  of  living  matter,  —  processes  summed  up 
in  that  famous  phrase  of  his  which  has  come  down  to  us  through 
the  Latin  of  the  middle  ages,  —  vis  medicatrix  natures,  —  "the 
healing  power  of  nature,"  one  of  the  finest  and  truest  of  the  tenets 
of  scientific  medicine  to-day.  Finally,  by  advancing  his  famous 
theory  of  the  four  humors,  a  theory  which  with  minor  modifications 
was  for  some  two  thousand  years  afterwards  the  prevailing  theory 
of  pathology,  or  the  nature  of  disease,  among  the  most  enlight- 
ened, Hippocrates  still  further  established  his  right  to  be  regarded 
as  the  "father"  of  medicine,  and  the  first  (and  only)  medical  man 
ever  authoritatively  entitled  "the  Great."  This  theory  —  crude 
enough  to-day  —  held  that  health  consists  in  the  right  mixture, 
and  disease  in  the  wrong  mixture,  of  four  "humors"  (juices) 
of  the  body,  viz.  blood,  phlegm,  yellow  bile,  and  black  bile.  Here 
again  the  great  merit  of  Hippocrates'  idea  was  that  it  directed 
attention  to  the  body  itself,  and  hence  to  natural  rather  than 
supernatural  phenomena. 

The  tone  of  the  Hippocratic  writings  is  well  illustrated  by  the 
titles  of  those  accepted  as  probably  genuine,  e.g.  On  Airs,  Waters, 
and  Places;  On  Epidemics;  On  Regimen  in  Acute  Diseases; 
On  Fractures;  On  Injuries  of  the  Head;  etc.  The  so-called 
Hippocratic  Oath  is  rightly  described  by  Gomperz  as  "a 
monument  of  the  highest  rank  in  the  history  of  civilization." 
That  this  oath  is  still  administered  to  graduates  about  to  enter  on 
the  practice  of  medicine,  is  sufficient  evidence  of  the  high  char- 
acter and  far-sighted  wisdom  of  its  originator.  (See  Appendix.) 

THE  SOPHISTS.  —  In  the  fifth  century  B.C.  political  events  fol- 
lowing war  with  Persia  made  Athens  supreme  in  Greece  —  the 


THE  GOLDEN  AGE  OF  GREECE         65 

finest  and  richest  city  in  the  world.  Its  citizens  aspired  to  suc- 
cess in  public  life,  and  sought  training  to  that  end  from  the  soph- 
ists. While  science  was  not  generally  cultivated  as  a  leading 
subject  in  the  educational  system  thus  developed,1  mathematics 
could  not  fail  to  be  esteemed  as  a  means  of  discipline,  and  several 
of  the  sophists  made  notable  contributions  to  its  development. 

HIPPIAS  OF  ELIS  is  the  first  sophist  to  be  mentioned  for  impor- 
tant mathematical  work.  About  420  B.C.  Hippias  invented  a 
curve  called  the  quadratrix,  serving  for  the  solution  of  two  of  the 
three  celebrated  problems  of  Greek  geometry ;  viz.  the  quadrature 
of  the  circle  and  the  trisection  of  an  angle.  By  means  of  straight 
line  and  circle  constructions,  the  solution  of  the  quadratic  equation 
had  been  accomplished,  though  without  algebraic  symbolism, 
or  any  recognition  of  negative  or  imaginary  results.  The  tri- 
section problem,  like  that  of  duplicating  the  cube,  was  equivalent 
to  the  solution  of  the  cubic  equation,  and  could  therefore  not  be 
accomplished  by  line  and  circle  methods. 
The  quadratrix  was  generated  by  the  inter- 
section P  of  two  moving  straight  lines,  one 
MQ  always  parallel  to  its  initial  position 
OA,  the  other  OR  revolving  uniformly  about 
a  centre  0.  By  means  of  this  curve  the 
trisection  problem  is  reduced  to  that  of  tri- 
secting a  straight  line,  which  is  elementary.2 
The  curve  meets  the  perpendicular  lines  OA  and  OB  at  C  and  B 
respectively  so  that  OC :  OB  =  2 :  TT,  where  TT  is  the  ratio  of  the 
circumference  of  a  circle  to  its  diameter.  To  this  quadrature 
solution  the  name  of  the  curve  is  due. 

Dinostratus  showed  that  the  assumptions  OC :  OB  >  2  :  TT  and 
OC:OB<2nr  both  lead  to  contradictions,  therefore  OC:OB  =  2:w 
—  a  good  example  of  the  Greek  reductio  ad  absurdum.  The 
study  of  a  problem  not  capable  of  solution  by  elementary  means 

1  See  Freeman,  "  Schools  of  Hellas." 

J  To  trisect  any  angle  as  AOR,  draw  MQ  parallel  to  OA  and  divide  OM  into  three 
equal  parts  by  lines  parallel  to  OA,  meeting  the  curve  in  D  and  E  respectively. 
The  radii  OS  and  OT  will  then  trisect  the  angle  AOQ,  by  the  definition  of  the  curve. 
F 


66  A  SHORT  HISTORY  OF  SCIENCE 

thus  led  to  the  invention  of  this  new  curve,  the  first  of  which 
we  have  any  definite  record. 

THE  CRITICISM  OF  ZENO.  —  The  Stoic  philosopher  Zeno,  teach- 
ing in  Athens  about  this  time,  though  not  himself  a  mathematician, 
represents  an  important  phase  of  philosophical  criticism  of  mathe- 
matics. Every  manifold,  he  says,  is  a  number  of  units,  but  a 
true  unit  is  indivisible.  Each  of  the  many  must  thus  be  itself 
an  indivisible  unit,  or  consist  of  such  units.  That  which  is  in- 
divisible however  can  have  no  magnitude,  for  everything  which 
has  magnitude  is  divisible  to  infinity.  The  separate  parts  have 
therefore  no  magnitude,  etc.  Again,  as  to  the  possibility  of  mo- 
tion, he  maintains  that  before  the  body  can  reach  its  destination 
it  must  reach  the  middle  point,  before  it  can  arrive  there  it  must 
traverse  the  quarter,  and  so  on  without  end.  Motion  is  thus 
impossible ;  so  the  tortoise,  if  he  have  any  start,  cannot  be  over- 
taken by  the  swift  runner  Achilles,  for  while  Achilles  is  covering 
that  distance  the  tortoise  will  have  attained  a  second  distance,  and 
so  on.  Such  specious  criticism  was  naturally,  and  in  a  measure 
justly,  evoked  by  misguided  efforts  of  certain  mathematicians  to 
show  that  a  line  consists  of  a  multitude  of  points,  etc.  These  or 
similar  controversies  as  to  the  interpretation  of  the  infinite  and 
the  infinitesimal  have  persisted  till  our  own  day,  resembling  in  that 
respect  the  classical  problems  of  circle  squaring  and  angle  tri- 
section  to  which  reference  has  been  made  above.  The  more  or  less 
mystical  statements  about  the  new  discoveries  of  the  Pythagoreans 
also  invited  sceptical  epigrams. 

Zeno  was  concerned  with  three  problems.  .  .  .  These  are  the 
problem  of  the  infinitesimal,  the  infinite,  and  continuity.  .  .  .  From 
him  to  our  own  day,  the  finest  intellects  of  each  generation  in  turn 
attacked  these  problems,  but  achieved,  broadly  speaking,  nothing.  .  .  . 

—  B.  Russell. 

Aristotle  accordingly  solves  the  problem  of  Zeno  the  Eleatic,  which 
he  propounded  to  Protagoras  the  Sophist.  Tell  me,  Protagoras,  said 
he,  does  one  grain  of  millet  make  a  noise  when  it  falls,  or  does  the 
ten-thousandth  part  of  a  grain?  On  receiving  the  answer  that  it 
does  not,  he  went  on :  Does  a  measure  of  millet  grains  make  a  noise 


THE  GOLDEN  AGE  OF  GREECE         67 

when  it  falls,  or  not?  He  answered,  it  does  make  a  noise.  Well, 
said  Zeno,  does  not  the  statement  about  the  measure  of  millet  apply 
to  the  one  grain  and  the  ten-thousandth  part  of  a  grain?  He  as- 
sented, and  Zeno  continued,  Are  not  the  statements  as  to  the  noise 
the  same  in  regard  to  each  ?  For  as  are  the  things  that  make  a  noise, 
so  are  the  noises.  Since  this  is  the  case,  if  the  measure  of  millet  makes 
a  noise,  the  one  grain  and  the  ten-thousandth  part  of  a  grain  make 
a  noise. 

CIRCLE  MEASUREMENT  :  ANTIPHON  AND  BRYSON  ;  HIPPOCRATES 
OF  CHIOS.  —  Two  of  the  sophists,  Antiphon  and  Bryson,  made 
an  interesting  contribution  to  the  problem  of  squaring  the  circle, 
by  means  of  the  inscribed  and  circumscribed  regular  polygons. 
Antiphon  started  with  a  regular  polygon  inscribed  in  a  circle, 
and  constructed  by  known  elementary  methods  an  equivalent 
square.  By  doubling  the  number  of  sides  repeatedly  he  obtained 
polygons  which  become  more  and  more  nearly  equivalent  to 
the  circle,  —  the  first  correct  attack  on  this  formidable  problem. 
Bryson  took  the  important  further  step  of  employing  both  in- 
scribed and  circumscribed  polygons,  making  however  the  not  un- 
natural assumption  that  the  area  of  the  circle  may  be  considered 
the  arithmetical  mean  between  them. 

Another  great  step  in  the  development  of  the  theory  of  the 
circle  was  accomplished  by  Hippocrates  of  Chios,  who  had  rela- 
tions with  the  now  dispersed  Pythagoreans  during  the  latter 
half  of  the  fifth  century  and  came  to  Athens  in  later  life 
after  financial  reverses.  He  is  said  in  the  register  of  mathe- 
maticians to  have  written  the  first  Elements  or  textbook  of 
mathematics,  in  which  he  made  effective  use  of  the  reductw 
ad  absurdum  as  a  method  of  relating  one  proposition  to 
another. 

To  Hippocrates  is  due  the  theorem  that  the  areas  of  circles  are 
proportional  to  the  squares  on  their  diameters.  He  appears  to 
have  employed  geometrical  figures  with  letters  at  the  vertices,  in 
the  modern  fashion.  From  the  theorem  in  regard  to  areas  of 
circles  follows  naturally  a  general  theorem  for  similar  segments 
and  sectors  of  circles.  His  work  on  lunes  is  remarkable.  Start- 


68  A  SHORT  HISTORY  OF  SCIENCE 

ing  with  an  isosceles  right  triangle,  he  describes  a  semicircle  on 
each  of  the  three  sides.  By  the  theorem  just  quoted  the  semi- 
circle on  the  hypotenuse  is  equal  in 
area  to  the  sum  of  the  other  two.  If 
the  larger  semicircle  is  taken  away 
from  the  entire  figure,  two  equal  lunes 
remain;  if  the  two  smaller  semi- 
circles are  taken  away,  the  triangle  remains.  Therefore  the 
two  lunes  are  together  equivalent  to  the  triangle,  and  the 
area  of  each  may  be  determined.  The  gulf  between  rectilin- 
ear and  curvilinear  figures  has  at  last  been  successfully  crossed. 
A  second  attempt  employs  three  equal  chords  instead  of  two,  and 
incidentally  the  theorem  that  the  square  on  the  side  of  a  triangle 
is  greater  than  the  sum  of  the  squares  on  the  other  two  sides  when 
the  angle  opposite  the  first  side  is  greater  than  a  right  angle. 
Other  interesting  and  still  more  complicated  attempts  are  pre- 
served. 

A  third  classical  problem  was  that  of  the  so-called  "  duplication 
of  the  cube."  One  of  the  older  Greek  tragedians  attributed  to 
King  Minos  the  words  referring  to  a  tomb  erected  at  his  order : 

Too  small  thou  hast  designed  me  the  royal  tomb, 
Double  it,  yet  fail  not  of  the  cube. 

At  a  somewhat  later  period  it  is  related  that  the  Delians,  suf- 
fering from  a  disease,  were  bidden  by  the  oracle  to  double  the  size 
of  one  of  their  altars,  and  invoked  the  aid  of  the  Athenian  geom- 
eters. Hippocrates  transformed  the  problem  of  solid  geometry 
into  one  in  two  dimensions  by  observing  that  it  is  equivalent  to 
that  of  inserting  two  geometrical  means  between  given  extremes. 
In  our  modern  algebraic  notation,  the  continued  proportion 
x:y  —  y:z  =  z:a  leads  to  the  equations  y2  =  xz,  zz  =  ya,  whence, 
eliminating  2,  y3  *=  ax2,  y  =  aV ;  y  and  z  are  the  desired  means 
between  x  and  a,  and  by  putting  a  =  2x  the  problem  is  solved. 
No  such  algebraic  notation  existed  at  this  time,  however, 
and  the  geometrical  methods  invented  by  later  Greek  mathema- 
ticians were  necessarily  very  complicated,  as  will  appear  below. 


THE  GOLDEN  AGE  OF  GREECE          69 

PLATO  AND  THE  ACADEMY.  —  One  of  the  greatest  names  in  the 
history  of  philosophy  is  that  of  Plato,  and  yet  with  Plato  philosophy 
enters  upon  a  new  phase  in  which  it  almost  parts  company  with 
science.  Before  Plato  philosophy  was  almost  wholly  devoted 
to  inquiries  or  speculations  touching  the  earth,  the  heavens,  and 
the  universe,  and  hence  was  substantially  "nature"  or  "natural" 
philosophy.  But  with  Plato  and  ever  since  his  time  the  larger 
part  of  philosophy  has  been  devoted  to  observation  and  specu- 
lation upon  the  human  mind  and  its  products,  and  has  accordingly 
often  been  called  "mental"  or  "moral"  as  contrasted  with  "nat- 
ural" philosophy.  It  is  therefore  Thales  and  Pythagoras,  Democ- 
ritus  and  Aristotle,  rather  than  Plato  and  his  disciples,  who  are 
the  protagonists  of  science  as  the  word  is  used  to-day. 

As  a  disciple  of  Socrates,  Plato  found  it  expedient  to  leave 
Athens  after  the  death  of  his  master,  and  during  the  following 
eleven  years  he  travelled  widely  in  the  Mediterranean  world, 
doubtless  familiarizing  himself  with  the  learning  of  Egypt  and  of 
the  Greek  Ptolemies.  After  having  been  sold  as  a  slave,  re- 
deemed and  set  free,  Plato  returned  to  his  native  city,  and  es- 
tablished himself  as  a  philosopher.  While  primarily  a  philosopher 
rather  than  a  mathematician,  Plato,  unlike  his  master  Socrates,  — 
who  desired  only  enough  mathematics  for  daily  needs,  —  rated 
highly  the  importance  of  mathematics  and  rendered  services  of 
the  greatest  value  in  its  development.  This  was  doubtless  due  in 
part  to  the  influence  of  Archytas,  a  friend  of  the  Pythagoreans,  with 
whom  he  had  associated  during  his  prolonged  exile. 

The  register  proceeds :  "Plato  .  .  .  caused  mathematics  in  gen- 
eral, and  geometry  in  particular,  to  make  great  advances,  by  reason 
of  his  well  known  zeal  for  the  study,  for  he  filled  his  writings  with 
mathematical  discourses,  and  on  every  occasion  exhibited  the 
remarkable  connection  between  mathematics  and  philosophy." 

"Let  no  one  ignorant  of  geometry  enter  under  my  roof"  was 
the  injunction  which  confronted  Plato's  would-be  disciples.  His 
respect  for  mathematics  finds  interesting  expression  in  the  re- 
marks he  puts  into  the  mouth  of  Socrates  in  the  Dialogues, 
and  to  him  it  is  largely  indebted  for  its  place  in  higher  education. 


70  A  SHORT  HISTORY  OF  SCIENCE 

In  the  Laws  he  advises  the  study  of  music  or  the  lyre  to  last 
from  the  age  of  13  years  to  16,  followed  by  mathematics,  weights  and 
measures,  and  the  astronomical  calendar  until  17.  For  a  few  picked 
boys  on  the  other  hand  in  the  Republic,  he  recommends  before  they 
are  18,  abstract  and  theoretical  mathematics,  theory  of  numbers, 
plane  and  solid  geometry,  kinetics,  and  harmonics.  Of  arithmetic 
he  says,  "Those  who  are  born  with  a  talent  for  it  are  quick  at 
learning,  while  even  those  who  are  slow  at  it  have  their  general 
intelligence  much  increased  by  studying  it."  "No  branch  of 
education  is  so  valuable  a  preparation  for  household  management 
and  politics  and  all  arts  and  crafts,  sciences  and  professions,  as 
arithmetic;  best  of  all  by  some  divine  art,  it  arouses  the  dull 
and  sleepy  brain,  and  makes  it  studious,  mindful,  and  sharp." 

The  geometrical  Greek  view  of  numbers,  exemplified  in  our 
use  of  square  and  cube  in  algebra,  is  well  illustrated  by  Thesetetus, 
who  says  to  Socrates  that  his  teacher 

was  giving  us  a  lesson  in  roots,  with  diagrams,  showing  us  that  the 
root  of  3  and  the  root  of  5  did  not  admit  of  linear  measurement  by  the 
foot  (that  is,  were  not  rational).  He  took  each  root  separately  up  to 
17.  There  as  it  happened  he  stopped,  so  the  other  pupil  and  I  de- 
termined, since  the  roots  were  apparently  infinite  in  number,  to  try 
to  find  a  single  name  which  would  embrace  all  these  roots.  We  di- 
vided all  numbers  into  two  parts.  The  number  which  has  a  square 
root  we  likened  to  the  geometrical  square,  and  called  'square  and 
equilateral'  (e.g.  4,  9,  16).  The  intermediate  numbers,  such  as  3  and 
5  and  the  rest  which  have  no  square  root,  but  are  made  up  of  unequal 
factors,  we  likened  to  the  rectangle  with  unequal  sides,  and  called 
rectangular  numbers. 

Under  Plato's  influence  mathematics  first  acquired  its  unified 
significance,  as  distinguished  from  geometry,  computation,  etc. 
Accurate  definitions  were  formulated,  questions  of  possibility 
considered,  methods  of  proof  criticized  and  systematized,  logi- 
cal rigor  insisted  upon.  The  philosophy  of  mathematics  was 
begun.  The  point  is  the  boundary  of  the  line ;  the  line  is  the 
boundary  of  the  surface ;  the  surface  is  the  boundary  of  the  solid. 


THE  GOLDEN  AGE  OF  GREECE          71 

Such  axioms  as  "Equals  subtracted  from  equals  leave  equals" 
date  from  this  period.  The  analytical  method  is  developed,  con- 
necting that  which  is  to  be  proved  with  that  which  is  already 
known.  Another  principle  carefully  observed  is  to  isolate  the 
problem  by  removing  all  non-essential  elements,  and  a  third  con- 
sists in  proving  that  assumptions  inconsistent  with  that  which  is 
to  be  proved  are  impossible. 

THE  ANALYTIC  METHOD.  —  The  analytic  method,  proceed- 
ing from  the  unknown  to  the  known,  depends  for  its  validity  on 
the  reversibility  of  the  steps ;  the  synthetic  method  on  the  contrary 
proceeds  from  the  known  to  the  unknown,  with  unimpeachable 
validity.  It  was  characteristic  of  the  Greek  geometers  to  aim 
at  this  form  for  their  demonstrations,  even  if  the  results  had  been 
first  obtained  analytically.  The  two  methods  are  well  illustrated 
by  the  following :  — 

A  circle  is  given  and  two  external  points  A  and  B.  It  is  required 
to  draw  straight  lines  AC  and  BC  meeting  the  circle  in  C,  D,  and  E 
so  that  DE  shall  be  parallel  to  AB.  It  is 
shown  that  if  the  construction  can  be  made, 
the  tangent  to  the  circle  at  D  will  meet  AB 
(produced  if  necessary)  in  a  point  F  which 
will  lie  on  a  new  circle  passing  through  A,  C, 
and  D.  This  analysis  of  consequences  is  the 
desired  clue  on  which  the  following  synthesis  F  "/A  B 

of  the  construction  is  then  based.     Starting 

again  with  A,  B  and  the  circle,  we  locate  F  so  that  BA  X  BF  = 
BC  X  BD  =  square  of  the  tangent  BG  from  B.  Then  drawing  a 
tangent  from  F  to  the  circle,  D  is  determined  and  with  it  the  re- 
quired line  DE. 

A  solution  of  the  "  duplication  of  the  cube  "  problem  is  also 
attributed  to  Plato,  though  the  mechanical  process  employed  is  so 
much  at  variance  with  his  usual  teachings  that  the  correctness  of 
the  attribution  is  seriously  questioned. 

SPQR  is  a  frame  in  which  SPQ  and  PQR  are  always  right  angles, 
while  PQ  may  be  varied,  and  SQ  and  PR  can  be  -revolved  about  Q 


72  A  SHORT  HISTORY  OF  SCIENCE 

and  P  respectively.  They  are  to  be  so  revolved  if  possible  that  they 
shall  cross  at  right  angles  at  T,  and  that  S  T  and  TR  shall  be  respect- 
ively equal  to  the  lengths  between  which  mean  pro- 
portionals are  to  be  inserted.  Then  by  similar  triangles 

ST:PT  =  PT:QT  =  QT:RT 

PT  and  QT  are  the  required  mean  proportionals.     If 
ST  is  taken  equal  to  twice  TR  the  special  case  of  the 
duplication  of  the  cube  is  represented. 

To  Plato  is  attributed  a  systematic  method  for  finding  numbers 
which  may  be  sides  of  right  triangles,  his  method  being  essentially 
an  extension  of  the  Pythagorean  already  described.  Plato's 
Timaeus  dialogue  is  indeed  an  important  source  of  our  information 
in  regard  to  Pythagorean  mathematics.  Plato  speaks  with  em- 
phatic scorn  of  the  shameful  ignorance  of  mensuration  on  the 
part  of  his  countrymen. 

He  is  unworthy  of  the  name  of  man  who  is  ignorant  of  the  fact 
that  the  diagonal  of  a  square  is  incommensurable  with  its  side. 

While  predominantly  interested  in  geometry,  Plato's  arithmetical 
attainments  were  considerable  for  his  time.  He  made,  for  ex- 
ample, a  correct  statement  about  the  59  divisions  of  5040. 

Arithmetic  has  a  very  great  and  elevating  effect,  compelling  the 
soul  to  reason  about  abstract  number,  and  if  visible  or  tangible  ob- 
jects are  obtruding  upon  the  argument,  refusing  to  be  satisfied. 

—  Plato,  Republic. 

...  It  would  be  proper  then,  Glaucon,  to  lay  down  laws  for 
this  branch  of  science  and  persuade  those  about  to  engage  in  the 
most  important  state-matters  to  apply  themselves  to  computation, 
and  study  it,  not  in  the  common  vulgar  fashion,  but  with  the  view 
of  arriving  at  the  contemplation  of  the  nature  of  numbers  by  the  in- 
tellect itself,  —  not  for  the  sake  of  buying  and  selling  as  anxious 
merchants  and  retailers,  but  for  war  also,  and  that  the  soul  may 
acquire  a  facility  in  turning  itself  from  what  is  in  the  course  of  gen- 
eration to  truth  and  real  being.  —  Plato,  Republic. 


THE  GOLDEN  AGE  OF  GREECE          73 

But  the  mathematical  "doctrines  concerning  the  parts  and  ele- 
ments of  the  Universe  are  put  forward  by  Plato,  not  so  much  as  as- 
sertions concerning  physical  facts,  of  which  the  truth  or  falsehood  is 
to  be  determined  by  a  reference  to  nature  herself.  They  are  rather 
propounded  as  examples  of  a  truth  of  a  higher  kind  than  any  refer- 
ence to  observation  can  give  or  can  test,  and  as  revelations  of  prin- 
ciples such  as  must  have  prevailed  in  the  mind  of  the  Creator  of  the 
universe ;  or  else  as  contemplations  by  which  the  mind  of  man  is  to 
be  raised  above  the  region  of  sense,  and  brought  nearer  to  the  Divine 
Mind.  —  Whewell. 

PLATONIC  COSMOLOGY.  —  The  spherical  figure  of  the  earth  was 
now  generally  accepted  in  Greece,  and  the  older  fanciful  cos- 
mogonies gradually  disappeared.  To  Plato,  whose  interest  in 
physical  science  was  indeed  but  secondary,  the  earth  was  a 
sphere  at  the  centre  of  the  universe,  requiring  no  support.  He 
supposes  the  distances  of  the  heavenly  bodies  to  be  proportional 
to  the  numbers :  Moon  1,  Sun  2,  Venus  3,  Mercury  4,  Mars  8, 
Jupiter  9,  Saturn  27,  —  these  numbers  being  obtained  by  com- 
bining the  arithmetic  and  geometric  progressions,  1,  2,  4,  8  and 
1,  3,  9,  27. 

Plato  accepts  as  a  principle  that  the  heavenly  bodies  move  with 
a  uniform  and  regular  circular  motion ;  he  then  proposes  to  the  mathe- 
maticians this  problem :  *  What  are  the  uniform  and  regular  circular 
motions  which  may  properly  be  taken  as  hypotheses  in  order  that 
we  may  save  the  appearances  presented  by  the  planets  ? ' 

His  general  conception  of  the  world  as  expressed  in  the  Timseus 
and  in  the  tenth  book  of  the  Republic  is  decidedly  mystical. 
In  the  latter  a  soul  returning  to  its  body  after  12  days  in  the  other 
world  relates  its  experiences  in  imaginative  language :  — 

Everyone  had  to  depart  on  the  eighth  day  and  to  arrive  at  a 
place  on  the  fourth  day  after,  whence  they  from  above  perceived  ex- 
tended through  the  whole  heaven  and  earth  a  light  as  a  pillar,  mostly 
resembling  the  rainbow,  only  more  splendid  and  clearer,  at  which 
they  arrived  in  one  day's  journey ;  and  there  they  perceived  in  the 
neighborhood  of  the  middle  of  the  light  of  heaven,  the  extremities  of 


74  A  SHORT  HISTORY  OF  SCIENCE 

the  ligatures  of  heaven  extended;  for  this  light  was  the  band  of 
heaven,  like  the  hawsers  of  triremes,  keeping  the  whole  circumference 
of  the  universe  together. 

Aristotle  sums  up  Plato's  theories  —  not  too  clearly  —  in  the 
words : 

In  a  similar  manner  the  Tim&us  shows  how  the  soul  moves  the 
body  because  it  is  interwoven  with  it.  For  consisting  of  the  elements 
and  divided  according  to  the  harmonic  numbers,  in  order  that  it 
might  have  an  innate  perception  of  harmony  and  that  the  universe 
might  move  in  corresponding  movements,  He  bent  its  straight  line 
into  a  circle,  and  having  by  division  made  two  doubly  joined  circles 
out  of  the  one  circle,  He  again  divided  one  of  them  into  seven  circles 
in  such  a  manner  that  the  motions  of  the  heavens  are  the  motions  of 
the  soul. 

Plato  probably  had  no  real  knowledge  of  those  deviations  of 
the  planets  from  uniform  circular  motion,  which  were  to  engross 
the  attention  of  succeeding  philosophers  and  astronomers.  His 
system  is  consistently  geocentric,  and  assumes  a  stationary 
earth.  According  to  Plutarch:  — 

Theophrastus  states  that  Plato,  when  he  was  old,  repented  of 
having  given  the  earth  the  central  place  in  the  universe  which  did 
not  belong  to  it, 

this  presumably  indicating  an  inclination  towards  the  theories 
of  the  later  Pythagoreans. 

Plato  adopts  the  Pythagorean  or  Empedoclean  hypothesis  of 
the  four  elements,  the  component  particles  being  assumed  to  have 
respectively  the  shapes  of  the  cube  (earth),  icosahedron  (water), 
octahedron  (air),  and  tetrahedron  (fire). 

All  the  heavenly  bodies  are  looked  on  as  divine  beings,  the  first  of 
all  living  creatures,  the  perfection  of  whose  minds  is  reflected  in  their 
orderly  motions. 

Summing  up  an  extended  discussion  of  Plato's  astronomical 
theories,  Dreyer  says :  — 


THE  GOLDEN  AGE  OF  GREECE         75 

There  is  absolutely  nothing  in  his  various  statements  about 
the  construction  of  the  universe  tending  to  show  that  he  had  de- 
voted much  time  to  the  details  of  the  heavenly  motions,  as  he  never 
goes  beyond  the  simplest  and  most  general  facts  regarding  the  revo- 
lutions of  the  planets.  Though  the  conception  of  the  world  as  Cos- 
mos, the  divine  work  of  art,  into  which  the  eternal  ideas  have  breathed 
life,  and  possessing  the  most  godlike  of  all  souls,  is  a  leading  feature 
in  his  philosophy,  the  details  of  scientific  research  had  probably  no 
great  attraction  for  him,  as  he  considered  mathematics  inferior  to 
pure  philosophy  in  that  it  assumes  certain  data  as  self-evident,  for 
which  reason  he  classes  it  as  superior  to  mere  opinion  but  less  clear 
than  real  science. 

Through  his  widely  read  books  he  helped  greatly  to  spread  the 
Pythagorean  doctrines  of  the  spherical  figure  of  the  earth  and  the 
orbital  motion  of  the  planets  from  west  to  east. 


The  conjunction  of  philosophical  and  mathematical  activity 
such  as  we  find,  beside  Plato,  only  in  Pythagoras,  Descartes  and 
Leibnitz,  has  always  borne  the  finest  fruits  for  mathematics.  To  the 
first  we  owe  scientific  mathematics  in  general.  Plato  discovered  the 
analytical  method,  through  which  mathematics  was  raised  above  the 
standpoint  of  the  Elements,  Descartes  created  analytic  geometry,  our 
own  celebrated  countryman  Leibnitz  the  infinitesimal  calculus,  — 
and  these  are  the  four  greatest  steps  in  the  development  of  mathe- 
matics. —  Hankel. 

ARCHYTAS.  —  To  Archytas,  a  late  Pythagorean,  with  whom 
Plato  had  had  close  relations,  was  due  the  earliest  solution  of  the 
duplication  problem.  This  very  interesting  and  somewhat  elab- 
orate solution  involves  a  combination  of  three  services,  a  cone  of 
revolution,  a  cylinder  having  the  vertex  of  the  cone  in  the  cir- 
cumference of  its  base,  and  a  surface  generated  by  revolving  a 
semicircle  about  an  axis  passing  through  one  end  of  its  diam- 
eter. It  shows  remarkable  mastery  of  elementary  geometry, 
both  plane  and  solid,  and  an  interesting  tendency  to  employ 
a  wider  range  of  methods,  including  motion,  which  might,  but 
for  adverse  tendencies,  have  had  important  results  in  connecting 
mathematics  with  its  possible  applications  to  mechanics,  etc. 
The  influence  of  Plato  in  avoiding  such  connections  and  asso- 


76  A  SHORT  HISTORY  OF  SCIENCE 

elating  geometry  with  abstract  logic  and  philosophy,  undoubtedly 
had  compensating  advantages  in  promoting  elegance  and  scien- 
tific rigor,  —  crystallizing  out  a  more  refined  product.  Archytas 
is  said  also  to  have  invented  the  screw  and  the  pulley  and  to  have 
been  the  first  to  give  a  systematic  treatment  of  mechanics,  employ- 
ing geometrical  theorems  for  this  purpose. 

MEN^ECHMUS  :  CONIC  SECTIONS.  —  Even  more  interesting  in 
its  foreshadowing  of  future  mathematical  developments  are  the 
solutions  of  the  duplication  problem  by  Mensechmus.  The 
problem  which  we  should  express  in  modern  algebraic  notation 
by  the  continued  proportion  a :  x :  :x:y:  :y:b,  Mensechmus,  with- 
out any  such  notation  or  any  system  of  coordinate  geometry,  shows 
to  be  equivalent  to  that  of  determining  the  intersection  either  of  a 
parabola  and  a  hyperbola,  corresponding  to  the  two  proportions 

a : x :  :x:y  and  a : x :  :y:b, 

or  to  the  intersection  of  two  parabolas,  in  case  the  second  pro- 
portion is  replaced  by  x :  y :  :y:b.  The  construction  of  either 
parabola  or  the  hyperbola  naturally  required  some  mechanical 
device. 

The  Greeks  of  this  period  distinguished  three  types  of 
the  cone  formed  by  the  rotation  of  the  right  triangle  about  one 
of  its  sides,  according  as  the  angle  formed  by  that  side  with  the 
hypotenuse  was  less  than,  equal  to,  or  greater  than  half  a  right 
angle.  A  plane  perpendicular  to  an  element  would  cut  a  cone  of 
the  first  kind  in  an  ellipse,  the  second  in  a  parabola,  the  third  in 
a  hyperbola.  These  curves  were  named  accordingly  sections  of 
the  acute-angled,  the  right-angled,  the  obtuse-angled  cone. 

The  discovery  of  the  conic  sections  .  .  .  first  threw  open  the 
higher  species  of  form  to  the  contemplation  of  geometers.  But  for 
this  discovery,  which  was  probably  regarded  ...  as  the  unprofitable 
amusement  of  a  speculative  brain,  the  whole  course  of  practical  phi- 
losophy of  the  present  day,  of  the  science  of  astronomy,  of  the  theory 
of  projectiles,  of  the  art  of  navigation,  might  have  run  in  a  different 
channel ;  and  the  greatest  discovery  that  has  ever  been  made  in  the 
history  of  the  world,  the  law  of  universal  gravitation,  with  its  in- 


THE  GOLDEN  AGE  OF  GREECE          77 

numerable  direct  and  indirect  consequences  and  applications  to  every 
department  of  human  research  and  industry,  might  never  to  this  hour 
have  been  elicited.  —  Sylvester. 

Many  of  Plato's  followers  and  disciples  in  the  Academy  con- 
tinued the  development  of  mathematics.  To  Xenocrates,  for 
example,  is  attributed  the  determination  of  the  number  of  all 
possible  syllables  as  1,002,000,000,000,  a  result  obtained  by 
some  unknown  method.  This  whole  period  is  one  of  great  pro- 
ductivity and  importance  in  the  history  of  mathematics.  New 
theorems  and  new  methods  are  discovered,  former  methods 
are  critically  scrutinized,  loci  problems  are  investigated,  these 
and  the  study  of  the  three  classical  problems  leading  to  the 
introduction  of  new  curves  and  a  general  extension  of  geo- 
metrical knowledge.  Geometry,  with  emphasis,  indeed,  on  its 
philosophical  side,  predominates  over  the  theory  of  numbers, 
and  even  the  latter  is  given  so  geometrical  a  form  that  mathe- 
matics is  unified. 

A  NEW  COSMOLOGY.  —  Eudoxus  of  Cnidos  (408  ?-355  B.C.) 
was  a  student  both  of  Archytas  and,  for  a  time,  of  Plato.  He  was 
not  only  mathematician  and  astronomer,  but  also  physician.  In 
mathematics  he  is  almost  a  new  creator  of  the  science,  developing 
the  theory  of  proportion,  making  a  special  study  of  the  "golden 
section,"  already  mentioned  in  connection  with  the  regular  poly- 
gons, and  obtaining  important  results  in  solid  geometry.  In  the 
words  of  the  register,  "Eudoxus  of  Cnidos  .  .  .  first  increased 
the  number  of  general  theorems,  added  to  the  three  propor- 
tions three  more,  and  raised  to  a  considerable  quantity  the  learn- 
ing begun  by  Plato  on  the  subject  of  the  (golden)  section,  to  which 
he  applied  the  analytical  method." 

To  him  was  formerly  attributed  the  proof  that  the  volume  of 
a  pyramid  is  one  third  that  of  the  prism  having  the  same  base 
and  altitude,  as  well  as  the  corresponding  theorem  for  cones  and 
cylinders.  A  recently  discovered  manuscript  of  Archimedes  shows, 
however,  that  for  this  Democritus  deserves  the  credit.  The 
method  of  exhaustion,  so-called,  employed  in  proving  these  theo- 


78  A  SHORT  HISTORY  OF  SCIENCE 

rems  was  expressed  in  the  auxiliary  theorem:  "When  two 
volumes  are  unequal,  it  is  possible  to  add  their  difference  to 
itself  so  many  times  that  the  result  shall  exceed  any  assigned 
finite  volume."  This  exceedingly  useful  and  important  princi- 
ple, avoiding  the  difficulties  of  infinitesimals,  was  expressed  in 
several  approximately  equivalent  forms,  and  was  already  im- 
plied in  the  work  of  Antiphon  and  Bryson.  A  solution  of  the 
duplication  problem  which  gained  Eudoxus  the  appellation 
"godlike"  has  been  entirely  lost. 

There  appear  to  have  been  no  astronomical  instruments  at  this 
tune  except  the  simple  gnomon  and  sun-dial,  but  the  more 
obvious  irregularities  of  the  planetary  motions  were  beginning  to 
attract  attention,  .and  under  Eudoxus  led  to  the  development  of 
a  new  and  important  theory.  Nearest  to  the  central  earth  is 
the  moon,  carried  on  the  equator  of  a  sphere  revolving  from  west 
to  east  in  27  days.  The  poles  of  this  sphere  are  themselves  car- 
ried on  a  second  sphere,  which  turns  in  about  18|  years  about 
the  axis  of  the  zodiac.  The  angle  between  the  axes  of  these  two 
spheres  corresponds  with  the  moon's  variation  in  latitude.  A 
third  outer  sphere  gives  the  daily  east  to  west  motion.  Simi- 
larly there  are  three  spheres  for  the  sun.  For  each  of  the  five 
planets  a  fourth  sphere  is  necessary  to  account  for  the  stations 
and  retrogressions  of  its  apparent  orbital  motion  —  thus  making 
with  the  single  sphere  of  the  stars  27  spheres,  all  having  their 
common  centre  at  the  centre  of  the  earth. 

How  far  these  spheres  were  regarded  as  having  concrete  exis- 
tence, how  far  they  merely  expressed  in  convenient  geometrical 
form  the  observed  relations  and  motions,  we  cannot  determine 
from  extant  evidence.  The  amount  of  observational  data  available 
was  entirely  inadequate  to  serve  as  a  basis  for  any  quantitatively 
correct  theory.  The  third  sphere  of  the  sun  was  based  on  an 
erroneous  hypothesis  as  to  its  motion.  For  Mercury,  Jupiter  and 
Saturn  the  theory  was  reasonably  adequate,  for  Venus  less  so,  and 
for  Mars  quite  defective. 

Calippus,  a  follower  of  Eudoxus,  endeavored  with  some  degree 
of  success  to  remedy  these  defects  by  adding  a  fifth  sphere  for 


THE  GOLDEN  AGE  OF  GREECE          79 

each  of  the  refractory  planets,  and  at  the  same  time  a  fourth  and 
fifth  for  the  sun,  in  order  to  account  for  the  recently  discovered 
inequality  in  the  length  of  the  four  seasons. 

Reviewing  the  development  of  this  interesting  theory,  Dreyer 
says :  — 

But  with  all  its  imperfections  as  to  detail,  the  theory  of  homo- 
centric  spheres  proposed  by  Eudoxus  demands  our  admiration  as  the 
first  serious  attempt  to  deal  with  the  apparently  lawless  motions  of  the 
planets.  .  .  .  Scientific  astronomy  may  really  be  said  to  date  from 
Eudoxus  and  Calippus,  as  we  here  for  the  first  time  meet  that  mutual 
influence  of  theory  and  observation  on  each  other  which  characterizes 
the  development  of  astronomy  from  century  to  century.  Eudoxus 
is  the  first  to  go  beyond  mere  philosophical  reasoning  about  the  con- 
struction of  the  universe ;  he  is  the  first  to  attempt  systematically  to 
account  for  the  planetary  motions.  When  he  has  done  this  the  next 
question  is  how  far  this  theory  satisfies  the  observed  phenomena,  and 
Calippus  at  once  supplies  the  observational  facts  required  to  test  the 
theory,  and  modifies  the  latter  until  the  theoretical  and  observed 
motions  agree  within  the  limits  of  accuracy  attainable  at  that  time. 
Philosophical  speculation  unsupported  by  steadily  pursued  obser- 
vations is  from  henceforth  abandoned:  the  science  of  astronomy 
has  started  on  its  career. 

Eudoxus  made  the  first  known  proposal  for  a  leap-year,  and  for 
a  star  catalogue.  A  marble  celestial  globe  in  the  national  museum 
at  Naples  is  perhaps  a  copy  of  one  made  by  him. 

ARISTOTLE,  384-322  B.C.,  "the  master  of  those  who  know,"  the 
son  of  a  physician,  a  student  in  Plato's  Academy,  and  tutor  of 
Alexander  the  Great,  exercised  a  mighty  and  lasting  influence  on 
the  development  of  Greek  science  and  philosophy.  His  tenden- 
cies were  mainly  non-mathematical,  but  the  theorem  that  the 
sum  of  the  exterior  angles  of  a  plane  polygon  is  four  right  angles 
is  ascribed  to  him.  He  distinguishes  sharply  between  geodesy  as 
an  art  and  geometry  as  a  science ;  he  considers  the  plane  sections 
of  the  circular  cyclinder;  he  recognizes  the  physical  reason  for 
the  adoption  of  ten  as  the  base  number  of  arithmetic ;  he  designates 
unknown  quantities  by  letters.  Continuity  —  an  idea  so  impor- 


80  A  SHORT  HISTORY  OF  SCIENCE 

tant  in  modern  mathematical  and  physical  science  —  he  defines 
by  saying :  — 

A  thing  is  continuous  when  of  any  two  successive  parts,  the  limits, 
at  which  they  touch,  are  one  and  the  same,  and  are,  as  the  word  im- 
plies, held  together. 

ARISTOTLE'S  MECHANICS.  —  In  mechanics  Aristotle  seems 
almost  to  recognize  the  principle  of  virtual  velocities.  He  dis- 
cusses the  composition  of  motions  at  an  angle  with  each  other. 
He  enunciates  the  correct  relation  between  the  length  of  the 
arms  of  a  lever  and  the  loads  which  will  balance  each  other 
upon  it.  He  even  deals  with  the  central  and  tangential  com- 
ponents of  circular  motion. 

He  asks  such  questions  as:  "Why  are  carriages  with  large 
wheels  easier  to  move  than  those  with  small  ?  "  "  Why  do  objects 
in  a  whirlpool  move  toward  the  center?"  etc. 

He  is  convinced  that  the  speed  of  falling  bodies  is  proportional 
to  their  weight  —  a  belief  credulously  accepted  until  Galileo's 
experiment  nineteen  centuries  later.  He  illustrates  his  discussions 
by  geometrical  figures,  and  states  correctly :  — 

If  a  be  a  force,  0  the  mass  to  which  it  is  applied,  y  the  distance 
through  which  it  is  moved,  and  5  the  time  of  the  motion,  then  a  will 
move  \  j8  through  2  y  in  the  time  5,  or  through  y  in  the  time  f  5. 

He  adds  erroneously,  however :  — 

It  does  not  follow  that  \  a  will  move  /?  through  \  y  in  the  time  5,  be- 
cause \  a  may  not  be  able  to  move  ft  at  all ;  for  100  men  may  drag 
a  ship  100  yards,  but  it  does  not  follow  that  one  man  can  drag  it 
one  yard. 

Of  the  bearing  of  Aristotle's  physical  theories  Duhem  says :  — 

Incapable  of  any  alteration,  inaccessible  to  any  violence,  the  celestial 
essence  could  manifest  no  other  than  its  own  natural  motion,  and 
that  was  uniform  rotation  about  the  centre  of  the  universe. 

Aristotle  is  the  author  of  eight  books  on  Physics,  four  on  the 
Heavens,  and  four  on  Meteorology.  In  physics  he  explains  the 
rainbow,  attributes  sound  to  atmospheric  motion,  and  discusses 


THE  GOLDEN  AGE  OF  GREECE          81 

refraction  mathematically.  While  he  undertakes  to  deal  with 
motion,  space  and  time  —  i.e.  with  the  subject-matter  of  me- 
chanics —  his  treatment  is  too  metaphysical  to  have  much  real 
value.  He  declares  for  example  that :  — 

The  bodies  of  which  the  world  is  composed  are  solids,  and 
therefore  have  three  dimensions.  Now,  three  is  the  most  per- 
fect number,  —  it  is  the  first  of  numbers,  for  of  one  we  do  not  speak 
as  a  number,  of  two  we  say  both,  three  is  the  first  number  of 
which  we  say  all.  Moreover,  it  has  a  beginning,  a  middle,  and  an 
end. 

Francis  Bacon  in  the  seventeenth  century  remarks  of 
Aristotle :  — 

Nor  let  any  one  be  moved  by  this ;  that  in  his  books  Of  Animals, 
and  in  his  Problems  and  in  others  of  his  tracts,  there  is  often  a  quoting 
of  experiments.  For  he  had  made  up  his  mind  beforehand ;  and 
did  not  consult  experience  in  order  to  make  right  propositions  and 
axioms,  but  when  he  had  settled  his  system  to  his  will,  he  twisted  ex- 
perience round,  and  made  her  bend  to  his  system ;  so  that  in  this  way 
he  is  even  more  wrong  than  his  modern  followers,  the  Schoolmen,  who 
have  deserted  experience  altogether. 

ARISTOTELIAN  ASTRONOMY.  —  Only  the  second  of  the  four 
books  on  the  Heavens  is  devoted  to  astronomy.  He  considers  the 
universe  to  be  spherical,  the  sphere  being  the  most  perfect  among 
solid  bodies,  and  the  only  body  which  can  revolve  in  its  own  space. 
Rotation  from  east  to  west  is  more  honorable  than  the  reverse. 
He  holds  that  the  stars  are  spherical  in  form,  that  they  have  no 
individual  motion,  being  merely  carried  all  together  by  their 
one  sphere. 

'  Furthermore,  since  the  stars  are  spherical,  as  others  maintain  and 
we  also  grant,  because  we  let  the  stars  be  produced  from  that  body, 
and  since  there  are  two  motions  of  a  spherical  body,  rolling  along  and 
whirling,  then  the  stars,  if  they  had  a  motion  of  their  own,  ought  to 
move  in  one  of  these  ways.  But  it  appears  that  they  move  in 
neither  of  these  ways.  For  if  they  whirled  (rotated),  they  would  re- 
main at  the  same  spot  and  not  alter  their  position,  and  yet  they 
manifestly  do  so,  and  everybody  says  they  do.  It  would  also  be 


82  A  SHORT  HISTORY  OF  SCIENCE 

reasonable  that  all  should  be  moved  in  the  same  motion,  and  yet 
among  the  stars  the  sun  only  seems  to  do  so  at  its  rising  or  setting, 
and  even  this  one  not  in  itself  but  only  owing  to  the  distance  of  our 
sight,  as  this  when  turned  on  a  very  distant  object  from  weakness 
becomes  shaky.  This  is  perhaps  also  the  reason  why  the  fixed  stars 
seem  to  twinkle,  while  the  planets  do  not  twinkle.  For  the  planets 
are  so  near  that  the  eyesight  reaches  them  in  its  full  power,  but  when 
turned  to  the  fixed  stars  it  shakes  on  account  of  the  distance,  be- 
cause it  is  aimed  at  too  distant  a  goal ;  now  its  shaking  makes  the 
motion  seem  to  belong  to  the  star,  for  it  makes  no  difference  whether 
one  lets  the  sight  or  the  seen  object  be  in  motion.  But  that  the 
stars  have  not  a  rolling  motion  is  evident ;  for  whatever  is  rolling 
must  of  necessity  be  turning,  while  of  the  moon  only  what  we  call  its 
face  is  visible/  —  Dreyer. 

Aristotle  adopts  the  system  of  spheres  of  Eudoxus  and 
Calippus,  but  seems  to  suppose  these  spheres  to  be  concrete,  and 
not  a  merely  geometrical  device  for  interpreting  the  phenomena 
or  determining  the  positions.  In  order  however  to  secure  what 
he  conceives  to  be  the  necessary  relation  between  the  motions  of 
the  spheres,  he  is  obliged  to  increase  their  total  number  from  33 
to  not  less  than  55.  The  earth  is  fixed  at  the  centre  of  the  uni- 
verse. That  the  earth  is  a  sphere  is  shown  logically,  and  is  also 
evident  to  the  senses.  During  eclipses  of  the  moon,  namely,  the 
boundary  line,  which  shows  the  shadow  of  the  earth,  is  always 
curved.  ...  If  we  travel  even  a  short  distance  south  or  north, 
the  stars  over  our  heads  show  a  great  change,  some  being  visible 
in  Egypt,  but  not  in  more  northern  lands,  and  stars  are  seen  to 
set  in  the  south  which  never  do  so  in  the  north.  It  seems  therefore 
not  incredible  that  the  vicinity  of  the  pillars  of  Hercules  is  con- 
nected with  that  of  India,  and  that  there  is  thus  but  one  ocean. 

The  bulk  of  the  earth  he  considers  to  be  "  not  large  in  compar- 
ison with  the  size  of  the  other  stars."  The  estimated  circumfer- 
ence of  400,000  stadia  —  about  39,000  miles  —  is  the  earliest  known 
estimate  of  the  size  of  the  earth,  and  is  of  unknown  origin,  but 
may  quite  likely  be  due  to  Eudoxus.  While  the  heavens  proper 
are  characterized  by  fixed  order  and  circular  motion,  the  space 


THE  GOLDEN  AGE  OF  GREECE         83 

below  the  moon's  sphere  is  subject  to  continual  change,  and  motions 
within  it  are  in  general  rectilinear  —  a  theory  destined  long  to 
block  progress  in  mechanics.  Of  the  four  elements,  earth  is  near- 
est the  centre,  water  comes  next,  fire  and  air  form  the  atmosphere, 
fire  predominating  in  the  upper  part,  air  in  the  lower.  In  this 
region  of  fire  are  generated  shooting  stars,  auroras,  and  comets, 
the  latter  consisting  of  ignited  vapors,  such  as  constitute  the 
Milky  Way. 

Against  any  orbital  motion  of  the  earth  Aristotle  urges  the  ab- 
sence of  any  apparent  displacement  of  the  stars.  Reviewing  his 
astronomical  theories,  Dreyer  says :  — 

His  careful  and  critical  examination  of  the  opinions  of  previous  phi- 
losophers makes  us  regret  all  the  more  that  his  search  for  the  causes 
of  .phenomena  was  often  a  mere  search  among  words,  a  series  of  vague 
and  loose  attempts  to  find  what  was  '  according  to  nature '  and  what 
was  not;  and  even  though  he  professed  to  found  his  speculations 
on  facts,  he  failed  to  free  his  discussion  of  these  from  purely  metaphys- 
ical and  preconceived  notions.  It  is,  however,  easy  to  understand 
the  great  veneration  in  which  his  voluminous  writings  on  natural 
science  were  held  for  so  many  centuries,  for  they  were  the  first,  and 
for  many  centuries  the  only,  attempt  to  systematize  the  whole 
amount  of  knowledge  of  nature  accessible  to  mankind;  while  the 
tendency  to  seek  for  the  principles  of  natural  philosophy  by  con- 
sidering the  meaning  of  the  words  ordinarily  used  to  describe  the 
phenomena  of  nature,  which  to  us  is  his  great  defect,  appealed  strongly 
to  the  mediaeval  mind,  and,  unfortunately,  finally  helped  to  retard 
the  development  of  science  in  the  days  of  Copernicus  and  Galileo. 

At  times  Aristotle  shows  consciousness  that  his  theories  are 
based  on  inadequate  knowledge  of  facts. 

'  The  phenomena  are  hot  yet  sufficiently  investigated.  When  they 
once  shall  be,  then  one  must  trust  more  to  observation  than  to  spec- 
ulation, and  to  the  latter  no  farther  than  it  agrees  with  the  phe- 
nomena.7 

'An  astronomer'  he  says  'must  be  the  wisest  of  men;  his  mind 
must  be  duly  disciplined  in  youth ;  especially  is  mathematical  study 
necessary ;  both  an  acquaintance  with  the  doctrine  of  number, 


84  A  SHORT  HISTORY  OF  SCIENCE 

and  also  with  that  other  branch  of  mathematics,  which,  closely  con- 
nected as  it  is  with  the  science  of  the  heavens,  we  very  absurdly  call 
geometry,  the  measurement  of  the  earth/ 

Aristotle's  writings  include  not  merely  works  on  scientific  sub- 
jects, but  treatises  of  the  very  first  importance  On  Poetry,  On 
Rhetoric,  On  Metaphysics,  On  Ethics,  and  On  Politics.  Besides 
his  scientific  works  mentioned  above,  there  are  others  entitled 
On  Generation  and  Destruction,  On  the  Parts  of  Animals, 
On  Generation  of  Animals,  Researches  about  Animals,  On  the 
Locomotion  of  Animals.  One  of  the  most  important  of  his 
many  services  to  science  is  the  encyclopedic  character  of  his 
writings,  since  from  time  to  time  he  reviews  in  them  the 
opinions  of  his  predecessors  whose  works  are  sometimes  known  to 
us  chiefly  through  his  references  to  them.  While  standing  thus 
upon  the  shoulders  of  the  past,  he  shows  at  the  same  time  both 
vast  learning  and  much  originality.  He  may  be  truly  called  the 
founder  of  zoology. 

Of  Aristotle's  contributions  to  science,  the  greatest  was  un- 
questionably that  spirit  of  curiosity,  of  inquiry,  of  scepticism,  and 
of  veracity  which  he  brought  to  bear  on  everything  about  him 
and  within  him.  His  observations  are  often  poor,  his  conclu- 
sions often  erroneous,  but  his  interest,  his  curiosity,  his  zeal  are 
indefatigable. 

THEOPHRASTUS.  —  One  of  Aristotle's  principal  pupils,  and  his 
successor  in  his  School,  was  Theophrastus  (372-287  B.C.)  notable 
in  the  history  of  science  chiefly  as  an  early  student  of  plants, 
and  writer  of  the  most  important  treatises  of  antiquity  on  botany. 
These  were  two  large  works,  one  of  ten  books  and  the  other  of 
•eight,  On  the  History  of  Plants,  and  On  the  Causes  of  Plants, 
respectively.  In  these,  more  than  500  species  of  plants  are  de- 
scribed, chiefly  with  reference  to  their  medicinal  uses.  It  is  es- 
pecially interesting  to  note  that  Theophrastus  recognized  the 
existence  of  sex  in  plants,  though  he  does  not  appear  to  have 
known  the  sex  organs. 

EPICURUS  AND  EPICUREANISM.  —  A  few  words  may  be  said  of 
another  philosopher  of  the  fourth  century,  a  follower  to  some 


THE  GOLDEN  AGE  OF  GREECE         85 

extent  of  Democritus  and  the  forerunner  and  exemplar  of  the 
Roman  Lucretius.  This  was  Epicurus  (342-270  B.C.),  who,  born 
in  Samos  and  educated  in  Athens  and  Asia  Minor,  became  a 
famous  teacher  and  the  head  of  a  remarkable  community  "such 
as  the  ancient  world  had  never  seen."  The  mode  of  life  in  this 
community  was  not  that  of  the  so-called  "epicures"  of  to-day,  but 
very  plain,  —  water  the  general  drink,  and  barley  bread  the 
general  food.  The  magnetic  personality  of  Epicurus  held  the 
community  together,  and  his  chief  work  was  a  treatise  on  Nature 
in  thirty-seven  books.  Epicureanism  is  of  interest  in  the  history 
of  science  chiefly  because  of  its  effect  on  its  Roman  exponent,  the 
poet  Lucretius.  Much  of  it  was  even  a  negation  of  science  and 
the  scientific  spirit. 

HERACLIDES.  ROTATION  OF  THE  EARTH.  —  To  Heraclides  of 
Pontus  in  the  fourth  century  B.C.  belongs  the  distinction  of  teach- 
ing that  the  earth  turns  on  its  own  axis  from  west  to  east  in  24 
hours.  He  had  been  connected  with  the  Pythagoreans,  and  with 
the  schools  of  Plato  and  Aristotle.  His  work  is  known  to  us  only 
indirectly,  none  of  his  own  writings  having  survived.  He  is  said 
also  to  have  advanced  the  hypothesis  that  Venus  and  Mercury 
revolve  about  the  sun,  being  therefore  at  a  distance  from  the 
earth  sometimes  greater  than  the  sun,  sometimes  less.  Geminus 
writing  in  the  first  half  of  the  first  century  B.C.  of  the  different 
fields  and  points  of  view  of  astronomers  and  physicists,  remarks :  — 

For  why  do  sun,  moon  and  planets  appear  to  move  unequally? 
Because,  when  we  assume  their  circles  to  be  excentric,  or  the  stars  to 
move  on  an  epicycle,  the  appearing  anomaly  can  be  accounted  for, 
and  it  is  necessary  to  investigate  in  how  many  ways  the  phenomena 
can  be  represented,  so  that  the  theory  of  the  wandering  stars  may  be 
made  to  agree  with  the  etiology  in  a  possible  manner.  Therefore  also 
a  certain  Heraclides  of  Pontus  stood  up  and  said  that  also  when  the 
earth  moved  in  some  way  and  the  sun  stood  still  in  some  way,  could 
the  irregularity  observed  relatively  to  the  sun  be  accounted  for. 
In  general  it  is  not  the  astronomer's  business  to  see  what  by  its  nature 
is  immovable  and  of  what  kind  the  moved  things  are,  but  framing 
hypotheses  as  to  some  things  being  in  motion  and  others  being  fixed, 


86  A  SHORT  HISTORY  OF  SCIENCE 

he  considers  which  hypotheses  are  in  conformity  with  the  phenomena 
in  the  heavens.  He  must  accept  as  his  principles  from  the  physicist, 
that  the  motions  of  the  stars  are  simple,  uniform,  and  regular,  of 
which  he  shows  that  the  revolutions  are  circular,  some  along  parallels, 
some  along  oblique  circles. 

This  contrast  between  the  physical  phenomena  and  the  mathe- 
matical theory  which  corresponds  with  them,  without  being  true 
or  perhaps  even  possible  in  all  respects,  is  of  continued  and  in- 
creasing importance  in  the  history  of  science,  as  a  larger  stock 
of  facts  was  accumulated  and  as  theories  still  imperfect  were  more 
frequently  subjected  to  critical  comparison  with  observed  data, 
instead  of  being  accepted  on  purely  philosophical  or  metaphysical 
grounds.  Heraclides  is  not  credited  with  any  conception  of 
orbital  or  progressive  motion  of  the  earth. 

REFERENCES  FOR  READING 

ALLMAN.     Greek  Geometry,  Chapters  III-IX. 
ARISTOTLE.     On  the  Parts  of  Animals,  On  Generation,  etc. 
BALL.     History  of  Mathematics,  Chapter  III. 
BUTCHER,  S.  H.     Aspects  of  the  Greek  Genius,  Chapter  I. 
BERRY.    -  History  of  Astronomy,  Chapter  II,  pp.  26-33. 
DREYER.     Planetary  System,  Chapters  III-V. 
FREEMAN,  K.  E.     Schools  of  Hellas. 

GARRISON,  F.  H.    A  History  of  Medicine.     (For  Hippocrates  of  Cos.) 
GOMPERZ.     Greek  Thinkers,  Vol.  I. 

Gow.     History  of  Greek  Mathematics,  Chapter  VI,  Articles  97-116. 
•  LEWES,  G.  H.     Aristotle,  a  Chapter  in  the  History  of  Science. 


CHAPTER  V 
GREEK  SCIENCE  IN  ALEXANDRIA 

There  is  an  astonishing  imagination,  even  in  the  science  of  mathe- 
matics. .  .  .  We  repeat,  there  was  far  more  imagination  in  the  head 
of  Archimedes  than  in  that  of  Homer.  —  Voltaire. 

If  the  Greeks  had  not  cultivated  Conic  Sections,  Kepler  could  not 
have  superseded  Ptolemy;  if  the  Greeks  had  cultivated  Dynamics, 
Kepler  might  have  anticipated  Newton.  —  Whewell. 

If  we  compare  a  mathematical  problem  with  an  immense  rock, 
whose  interior  we  wish  to  penetrate,  then  the  work  of  the  Greek 
mathematicians  appears  to  us  like  that  of  a  robust  stonecutter,  who, 
with  indefatigable  perseverance,  attempts  to  demolish  the  rock 
gradually  from  the  outsideJlfr  means  of  hammer  and  chisel  ;  but  the 
modern  mathematician^MRmbles  an  expert  miner,  who  first  con- 
structs a  few  passage^HRigh  the  rock  and  then  explodes  it  with  a 
single  blast,  bringinght  its  inner  treasures.  —  Hankel. 


THE  MusEpjLEXANDRiA.  —  The  subjugation  of  Greece 
by  Alexander  'xhe'Great  in  330  B.C.  checked  the  further  develop- 
ment of  Greek  civilization  on  its  native  soil.  After  Alexander's 
death  in  323,  his  vast  empire  was  divided  among  his  generals,  and 
Alexandria,  the  new  Egyptian  capital,  fell  to  the  lot  of  Ptolemy. 
The  city  as  such  was  then  barely  ten  years  old,  but  very  soon 
became,  under  the  rule  of  the  Ptolemies,  the  centre  of  the  learned 
world.  By  300  B.C.  the  Museum  (Seat  of  the  Muses)  was 
founded,  becoming  in  effect  a  veritable  university  of  Greek  learning. 
To  this  were  attached  a  great  library,  a  dining  hall,  and  lecture- 
rooms  for  professors.  Here  for  the  next  700  years  Greek  science 
had  its  chief  abiding  place.  The  fame  of  Alexandria  soon  out- 
shone and  eventually  eclipsed  that  of  Athens,  while  Romans 
journeyed  from  Rome  —  never  important  in  ancient  times  as  a 

87 


88  A  SHORT  HISTORY  OF  SCIENCE 

scientific  centre  —  to  study  at  Alexandria  the  healing  art,  anatomy, 
mathematical  science,  geography,  and  astronomy.  Neither 
Athens,  Rome,  Carthage,  nor  any  other  city  of  the  ancient  world 
can  boast  similar  distinction  as  a  home  of  science. 

EUCLID.  —  Three  centuries  after  Thales  had  introduced  the 
rudiments  of  Egyptian  mathematics  into  Greece,  the  focus  of 
mathematical  activity  was  again  transferred  to  that  ancient  land, 
but  its  spirit  and  aims  remained  there  still  for  centuries  essentially 
Greek.  Continuing  the  ancient  register,  Proclus  writes :  — 

Not  much  younger  than  these  (the  Aristotelians)  is  Euclid,  who 
brought  the  elements  together,  arranged  much  of  the  work  of  Eudoxus 
in  complete  form,  and  brought  much  which  had  been  begun  by 
Theaetetus  to  completion.  Besides  he  supported  what  had  been  only 
partially  proved  by  his  predecessors  with  irrefragable  proofs.  .  .  . 
It  is  related  that  King  Ptolemy  asked  him  once  if  there  were  not  in 
geometrical  matters  a  shorter  way  than  through  the  Elements :  to 
which  he  replied  that  in  geometry  there  is  no  straight  path  for 
kings.  .  .  . 

As  a  recent  writer  has  well  said :  "  There  are  royal  roads  in 
science ;  but  those  who  first  tread  them  are  men  of  genius  and  not 
kings."  % 

Euclid's  period  of  activity  was  about  300  B.C.  ;  his  place  of  birth 
and  even  his  race  are  unknown;  he  is  said  to  have  been  of  a 
mild  and  benevolent  disposition,  and  to  have  appreciated  fully 
the  scientific  merits  of  his  predecessors.  While  we  know  next 
to  nothing  of  his  life  and  personality,  his  writings  have  had 
an  influence  and  a  prolonged  vitality  almost,  if  not  quite,  unpar- 
alleled. 

EUCLID'S  "ELEMENTS."  —  Scientifically,  Euclid  is  attached  to 
the  Platonic  philosophy.  Thus  he  makes  the  goal  of  his  Elements 
the  construction  of  the  so-called  "Platonic  bodies"  i.e.,  the  five 
regular  polyhedrons.  This  treatise,  which  served  as  the  basis  of 
practically  all  elementary  instruction  for  the  following  2000  years, 
is  naturally  his  best-known  work,  and  appears  to  have  been  ac- 
cepted in  the  Greek  world  after  many  previous  attempts  as  a 


GREEK  SCIENCE  IN  ALEXANDRIA  89 

finality.  It  consisted  of  thirteen  books,  of  which  only  the 
first  six  are  ordinarily  included  in  modern  editions.  The  whole 
is  essentially  a  systematic  introduction  to  Greek  mathematics, 
consisting  mainly  of  a  comparative  study  of  the  properties  and 
relations  of  those  geometrical  figures,  both  plane  and  solid,  which 
can  be  constructed  with  ruler  and  compass.  The  comparison  of 
unequal  figures  leads  to  arithmetical  discussion,  including  the 
consideration  of  irrational  numbers  corresponding  to  incommensu- 
rable lines.  The  contents  may  be  briefly  summarized  as  follows : 
Book  I  deals  with  triangles  and  the  theory  of  parallels :  Book  II 
with  applications  of  the  Pythagorean  theorem,  many  of  the  prop- 
ositions being  equivalent  to  algebraic  identities,  or  solutions  of 
quadratic  equations,  which  seem  to  us  more  simple  and  obvious 
than  to  the  Greeks.  It  should  be  noted  however  that  the  geomet- 
rical treatment  is  relatively  advantageous  for  oral  presentation. 
Book  III  deals  with  the  circle,  Book  IV  with  inscribed  and  cir- 
cumscribed polygons.  These  first  four  books  thus  contain  a 
general  treatment  of  the  simpler  geometrical  figures,  together 
with  an  elementary  arithmetic  and  algebra  of  geometrical  magni- 
tudes. In  Book  V,  for  lack  of  an  independent  Greek  arithmetical 
analysis,  a  theory  of  proportion  (which  has  thus  far  been 
avoided)  is  worked  out,  with  the  various  possible  forms  of  the 

equation  -  =  -  •     The  results  are  applied  in  Book  VI  to  the  com- 
b      a 

parison  of  similar  figures.  This  contains  the  first  known  problem 
in  maxima  and  minima,  —  the  square  is  the  greatest  rectangle 
of  given  perimeter,  —  also  geometrical  equivalents  of  the  solution 
of  quadratic  equations.  The  next  three  Books  are  devoted  to  the 
theory  of  numbers,  including  for  example  the  study  of  prime  and 
composite  numbers,  of  numbers  in  proportion,  and  the  determina- 
tion of  the  greatest  common  divisor.  He  shows  how  to  find  the 
sum  of  a  geometrical  progression,  and  proves  that  the  number  of 
prime  numbers  is  infinite. 

If  there  were  a  largest  prime  number  n  then  the  product  1  X  2  X 
3  ...  X  n  increased  by  1  would  always  leave  a  remainder  1  when  di- 
vided by  n  or  by  any  smaller  number.  It  would  thus  either  be  prune 


90  A  SHORT  HISTORY  OF  SCIENCE 

itself,  or  a  product  of  prime  factors  greater  than  n,  either  of 
which  suppositions  is  contrary  to  the  hypothesis  that  n  itself  is  the 
greatest  prime  number. 

Book  X  deals  with  the  incommensurable  on  the  basis  of  the 
theorem :  If  two  unequal  magnitudes  are  given,  and  if  one  takes 
from  the  greater  more  than  its  half,  and  from  the  remainder  more 
than  its  half  and  so  on,  one  arrives  sooner  or  later  at  a  remainder 
which  is  less  than  the  smaller  given  magnitude.  Books  XI,  XII, 
and  XIII  are  devoted  to  solid  geometry,  leading  up  to  our  familiar 
theorems  on  the  volume  of  prism,  pyramid,  cylinder,  cone,  and 
sphere,  but  in  every  case  without  computation,  emphasizing  the 
habitual  distinction  between  geometry  and  geodesy  or  mensura- 
tion ...  a  distinction  expressed  by  Aristotle  in  the  form  :  "  One 
cannot  prove  anything  by  starting  from  another  species,  for  ex- 
ample, anything  geometrical  by  means  of  arithmetic.  Where 
the  objects  are  so  different  as  arithmetic  and  geometry  one  cannot 
apply  the  arithmetical  method  to  that  which  belongs  to  magni- 
tudes in  general,  unless  the  magnitudes  are  numbers,  which  can 
happen  only  in  certain  cases."  Book  XIII  passes  from  the 
regular  polygons  to  the  regular  polyhedrons,  remarking  in  con- 
clusion that  only  the  known  five  are  possible. 

The  extent  to  which  Euclid's  Elements  represent  original  work 
rather  than  compilation  of  that  of  earlier  writers  cannot  be  deter- 
mined. It  would  appear,  for  example,  that  much  of  Books  I  and 
II  is  due  to  Pythagoras,  of  III  to  Hippocrates,  of  V  to  Eudoxus, 
and  of  IV,  VI,  XI,  and  XII,  to  later  Greek  writers ;  but  the  work 
as  a  whole  constitutes  an  immense  advance  over  previous  similar 
attempts. 

Proclus  (410-485  A.D.)  is  the  earliest  extant  source  of  informa- 
tion about  Euclid.  Theon  of  Alexandria  edited  the  Elements 
nearly  700  years  after  Euclid,  and  until  comparatively  recent 
times  modern  editions  have  been  based  upon  his. 

Like  other  Greek  learning,  Euclid  has  come  down  to  later  times 
through  Arab  channels.  There  is  a  doubtful  tradition  that  an 
English  monk,  Adelhard  of  Bath,  surreptitiously  made  a  Latin 


GREEK  SCIENCE   IN  ALEXANDRIA  91 

translation  of  the  Elements  at  a  Moorish  university  in  Spain 
in  1120.  Another  dates  from  1185,  printed  copies  from  1482  on- 
ward, and  an  English  version  from  1570.  After  Newton's  time 
it  found  its  way  from  the  universities  into  the  lower  schools. 

Different  versions  vary  widely  as  to  the  axioms  and  postulates 
on  which  the  work  as  a  whole  is  based.  It  is  believed  that  Euclid 
originally  wrote  five  postulates,  of  which  the  fourth  and  fifth  are 
now  known  as  Axioms  11  and  12,  —  "All  right  angles  are  equal  "  ; 
and  the  famous  parallel  axiom :  —  "If  a  straight  line  meets  two 
straight  lines,  so  as  to  make  the  two  interior  angles  on  the  same 
side  of  it  together  less  than  two  right  angles,  these  straight  lines 
will  meet  if  produced  on  that  side."  The  necessarily  unsuccess- 
ful attempts  which  have  since  been  made  to  prove  this  as  a 
proposition  rather  than  a  postulate  constitute  an  important 
chapter  in  the  history  of  mathematics,  leading  in  the  last  century 
to  the  invention  of  the  generalized  geometry  known  as  non- 
Euclidean,  in  which  this  axiom  is  no  longer  valid. 

INFLUENCE  OF  EUCLID.  —  The  Elements  of  Euclid  have  exerted 
an  immense  influence  on  the  development  of  mathematics,  and 
particularly  of  mathematical  pedagogy.  '  Aside  from  their  sub- 
stance of  geometrical  facts,  they  are  characterized  by  a  strict 
conformity  to  a  definite  logical  form,  the  formulation  of  what  is 
to  be  proved,  the  hypothesis,  the  construction,  the  progressive 
reasoning  leading  .from  the  known  to  the  unknown,  ending  with 
the  familiar  Q.E.D.  There  is  a  careful  avoidance  of  whatever 
is  not  geometrical.  No  attempt  is  made  to  develop  initiative 
or  invention  on  the  part  of  the  student ;  the  manner  in  which  the 
results  have  been  discovered  is  rarely  evident  and  is  even  some- 
times concealed ;  each  proposition  has  a  degree  of  completeness 
in  itself.  This  treatise  translated  into  the  languages  of  modern 
Europe  has  been  a  remarkable  means  of  disciplinary  training  in 
its  special  form  of  logic.  No  other  science  has  had  any  such  single 
permanently  authoritative  treatise. 

CRITICISM  OF  EUCLID.  —  On  the  other  hand,  its  narrowness  of 
aim,  its  deliberate  exclusion  of  the  concrete,  its  laborious  methods 
of  dealing  with  such  matters  as  infinity,  the  incommensurable  or 


92  A  SHORT  HISTORY  OF  SCIENCE 

irrational,  its  imperfect  substitutes  for  algebra,  as  in  the  theory 
of  proportion,  have  diminished  its  usefulness,  and  have  in  com- 
paratively recent  times  (in  English-speaking  countries)  led  to  the 
substitution  of  modernized  texts.  Still,  no  other  mathematical 
treatise  has  had  even  approximately  the  deservedly  far-reaching 
influence  of  Euclid.  Its  subject-matter  is  so  nearly  complete 
that  its  author's  name  is  still  a  current  synonym  for  elementary 
geometry. 

His  elements  are  particularly  admired  for  the  order  which  con- 
trols them,  for  the  choice  of  theorems  and  problems  selected  as  funda- 
mental (for  he  has  by  no  means  inserted  all  which  he  might  give, 
but  only  those  which  are  really  fundamental),  and  for  the  varied 
argumentation,  producing  conviction  now  by  starting  from  causes, 
now  by  going  back  to  facts,  but  always  irrefutable,  exact  and  of  most 
scientific  character.  .  .  .  Shall  we  mention  the  constantly  main- 
tained invention,  economy  and  orderliness,  the  force  with  which  he 
establishes  every  point?  If  one  adds  to  or  takes  from  it,  one  will 
recognize  that  he  departs  thereby  from  science,  tending  towards  error 
or  ignorance.  .  .  . 

Elsewhere  Proclus :  — 

It  is  difficult  in  every  science  to  choose  and  dispose  in  suitable 
order  the  elements  from  which  all  the  rest  may  be  derived.  Of  those 
who  have  attempted  this  some  have  increased  their  collection,  others 
have  diminished  it ;  some  have  employed  abridged  demonstrations, 
others  have  expanded  their  presentation  indefinitely,  etc. 

In  such  a  treatise  it  is  necessary  to  avoid  everything  superfluous 
...  to  combine  all  that  is  essential,  to  consider  principally  and 
equally  clearness  and  brevity,  to  give  theorems  their  most  general 
form,  —  for  the  detail  of  teaching  particular  cases  only  makes  the 
acquisition  of  knowledge  more  difficult.  From  all  these  points  of 
view,  Euclid's  Elements  will  be  found  superior  to  every  other. 

In  a  recent  interesting  discussion  of  Euclid's  Elements,  F.  Klein 
(Elementar-Mathematik  vom  Hoheren  Standpunkt  aus.  II)  says  in 
substance :  "A  false  estimation  of  the  Elements  finds  its  source 
in  the  general  misunderstanding  of  Greek  genius  which  long  pre- 


GREEK  SCIENCE  IN  ALEXANDRIA  93 

vailed  and  still  finds  popular  acceptance,  namely  that  Greek 
culture  was  confined  to  relatively  few  fields,  but  in  them  reached 
a  high  degree  of  perfection  and  finality.  The  fact  is,  however,  that 
the  Greeks  occupied  themselves  with  the  greatest  versatility  in  all 
directions,  and  made  in  all  directions  wonderful  progress.  Never- 
theless, from  our  modern  standpoint,  they  fell  short  of  the  pos- 
sibly attainable  in  all,  and  in  some  directions  made  only  a  begin- 
ning. 

"  In  mathematics,  for  example,  it  has  become  a  tradition  that 
Greek  geometry  reached  unique  development,  while  in  reality 
many  other  branches  of  mathematics  were  successfully  cultivated. 
The  development  of  Greek  mathematics  was  particularly  ham- 
pered by  the  lack  of  a  convenient  number-system  and  notation 
as  a  basis  for  an  independent  arithmetic,  and  by  ignorance  of 
negative  and  imaginary  numbers.  Euclid's  intention  in  the  Ele- 
ments was  by  no  means  to  write  an  encyclopedia  of  current  geom- 
etry, which  must  have  included  conic  sections  and  other  curves, 
but  rather  to  write  for  mature  readers  an  introduction  to  mathe- 
matics in  general,  the  latter  being  regarded  in  its  turn,  in  the 
Platonic  sense,  as  necessary  preparation  for  general  philosophic 
studies.  Hence  the  emphasis  on  formal  order  and  logical  method, 
as  well  as  the  omission  of  all  practical  applications.  He  aims  at 
the  flawless  logical  derivation  of  all  geometrical  theorems  from 
premises  completely  stated  in  advance." 

Allowing  for  grave  uncertainties  of  text,  Klein's  view  is  summed 
up  as  follows : 

"(1)  The  great  historical  significance  of  Euclid's  Elements 
consists  in  the  fact  that  through  it  the  ideal  of  a  flawless  logical 
treatment  of  geometry  was  first  transmitted  to  future  times. 

"  (2)  As  to  the  execution,  much  is  very  finely  done,  but  much 
remains  fundamentally  imperfect  from  our  present  standpoint. 

"  (3)  Numerous  details  of  importance,  especially  at  the  begin- 
ning, remain  completely  doubtful  on  account  of  uncertainties  of 
the  text. 

"(4)  The  whole  development  is  often  needlessly  clumsy,  as 
Euclid  has  no  arithmetic  ready  to  his  hand. 


94  A  SHORT  HISTORY  OF  SCIENCE 

"(5)  In  general  the  one-sided  emphasis  on  the  logical  makes 
it  difficult  to  understand  the  subject-matter  as  a  whole,  and  its 
internal  relations." 

The  Elements  of  the  great  Alexandrian  remain  for  all  time  the 
first,  and  one  may  venture  to  assert,  the  only  perfect  model  of  logical 
exactness  of  principles,  and  of  rigorous  development  of  theorems. 
If  one  would  see  how  a  science  can  be  constructed  and  developed  to 
its  minutest  details  from  a  very  small  number  of  intuitively  per- 
ceived axioms,  postulates,  .and  plain  definitions,  by  means  of  rigorous, 
one  would  almost  say  chaste,  syllogism,  which  nowhere  makes  use 
of  surreptitious  or  foreign  aids,  if  one  would  see  how  a  science  may 
thus  be  constructed,  one  must  turn  to  the  Elements  of  Euclid. 
—  Hankel. 

Euclid  always  contemplates  a  straight  line  as  drawn  between  two 
definite  points,  and  is  very  careful  to  mention  when  it  is  to  be  pro- 
duced beyond  this  segment.  He  never  thinks  of  the  line  as  an  entity 
given  once  for  all  as  a  whole.  This  careful  definition  and  limitation, 
so  as  to  exclude  an  infinity  not  immediately  apparent  to  the  senses, 
was  very  characteristic  of  the  Greeks  in  all  their  many  activities. 
It  is  enshrined  in  the  difference  between  Greek  architecture  and  Gothic 
architecture,  and  between  the  Greek  religion  and  the  modern  religion. 
The  spire  on  a  Gothic  cathedral  and  the  importance  of  the  unbounded 
straight  line  in  modern  geometry  are  both  emblematic  of  the  trans- 
formation of  the  modern  world.  —  Whitehead. 

The  universally  admired  perfection  of  the  work  of  Euclid  is  re- 
vealed to  the  historians  as  the  natural  product  of  a  long  criticism 
which  was  developed  in  the  constructive  period  of  rational  geometry, 
from  Pythagoras  to  Eudoxus.  Then  commenced  to  appear  the  signifi- 
cation of  those  methods  and  principles  by  means  of  which  the  Greeks 
themselves  attempted  to  interpret  and  conquer  the  paradoxes .  con- 
cerning infinity.  These  are  the  same  difficulties  which  reappeared 
at  the  time  the  infinitesimal  calculus  was  founded,  and  are  now  again 
asserting  themselves  in  the  most  refined  analysis.  —  Enriques. 

OTHER  WORKS  OF  EUCLID.  —  Besides  the  "Elements"  Euclid 
wrote  several  other  mathematical  treatises,  including  one  on 
Porisms,  a  special  type  of  geometrical  proposition;  and  one  on 
Data,  containing  such  theorems  as  the  following : 


GREEK  SCIENCE  IN  ALEXANDRIA  95 

Given  magnitudes  have  a  given  ratio  to  each  other. 

When  two  lines  given  in  position  cut  each  other  their  point  of 
intersection  is  given. 

When  in  a  circle  of  given  magnitude  a  line  of  given  magnitude 
is  given,  it  bounds  a  segment  which  contains  a  given  angle. 

A  work  on  Fallacies  is  designed  to  safeguard  the  student  against 
erroneous  reasoning.  Still  other  treatises  are  devoted  to  Division 
of  Figures,  Loci,  and  Conic  Sections ;  finally  there  are  works  on 
Phenomena,  on  Optics,  and  on  Catoptrics  dealing  with  applica- 
tions of  geometry. 

The  Phenomena  gives  a  geometrical  theory  of  the  universe,  the 
Optics  is  an  unsuccessful  attempt  to  deal  with  problems  of  vision 
on  the  hypothesis  that  light  proceeds  from  the  eye  to  the  object 
seen.  The  fundamental  assumptions  are,  for  example :  "  Rays 
emitted  from  the  eye  are  carried  in  straight  lines,  distant  by  an 
interval  from  one  another, "  etc. 

The  Catoptrics  deals  in  31  propositions  with  reflections  in  plane, 
concave,  and  convex  mirrors.  It  is  remarked  that  a  ring  placed 
in  a  vase  so  as  to  be  invisible  from  a  certain  position,  may  be  made 
visible  by  filling  the  vase  with  water.  The  authenticity  of  this 
work  is  however  questionable. 

These  two  works  constitute  the  earliest  known  attempt  to 
apply  geometry  systematically  to  the  phenomena  of  light-rays. 
The  law  of  reflection  is  correctly  applied.  Just  as  geometry  is 
based  on  a  definite  list  of  axioms,  so  Euclid  makes  his  optics 
depend  on  eight  fundamental  facts  of  experience.  For  example, 
the  light  rays  are  straight  lines.  The  figure  inclosed  by  the  rays 
is  a  cone  with  its  vertex  at  the  eye,  while  the  boundary  of  the 
object  corresponds  to  the  base,  etc.  This  work,  though  in  very 
imperfect  form,  continued  in  use  until  Kepler's  time. 

ARCHIMEDES.  —  The  second  great  name  in  the  Alexandrian 
school  and  one  of  the  greatest  in  the  whole  history  of  science  is 
that  of  Archimedes.  He  was  both  geometer  and  analyst,  mathe- 
matician and  engineer.  He  enriched  even  the  highly  developed 
Euclidean  geometry,  made  important  progress  in  algebra,  laid  the 
foundations  of  mechanics,  and  even  anticipated  the  infinitesimal 


96  A  SHORT  HISTORY  OF  SCIENCE 

calculus,  reaching  thus  a  level  which  was  not  surpassed  for  2000 
years.  Born  in  Syracuse,  probably  287  B.C.,  the  greater  part  of 
his  life  was  spent  in  his  native  city,  to  which  he  rendered  on  oc- 
casion invaluable  services  as  a  military  engineer.  According  to 
Livy  it  was  due  to  the  efforts  of  Archimedes  that  the  Romans 
.under  Marcellus  were  held  in  check  during  the  protracted  siege 
of  Syracuse.  On  the  fall  of  the  city  in  212  B.C.  the  venerable 
mathematician,  absorbed  in  a  geometrical  problem,  was  killed  by 
a  Roman  soldier,  much  to  the  regret  of  Marcellus,  who  appre- 
ciated and  would  have  spared  him.  The  conqueror  carried  out 
the  wish  of  Archimedes  by  erecting  a  monument  with  a  mathe- 
matical figure,  and  this  was  with  some  difficulty  rediscovered  and 
put  in  order  by  Cicero,  during  his  official  residence  in  Sicily,  75  B.C. 

Nothing  afflicted  Marcellus  so  much  as  the  death  of  Archimedes, 
who  was  then,  as  fate  would  have  it,  intent  upon  working  out  some 
problem  by  a  diagram,  and  having  fixed  his  mind  alike  and  his  eyes 
upon  the  subject  of  his  speculation,  he  never  noticed  the  incursion 
of  the  Romans,  nor  that  the  city  was  taken.  In  this  transport  of 
study  and  contemplation,  a  soldier,  unexpectedly  coming  up  to  him 
commanded  him  to  follow  to  Marcellus,  which  he  declined  to  do  be- 
fore he  had  worked  out  his  problem  to  a  demonstration ;  the  soldier, 
enraged,  drew  his  sword  and  ran  him  through.  Others  write,  that  a 
Roman  soldier,  running  upon  him  with  a  drawn  sword,  offered  to  kill 
him ;  and  that  Archimedes,  looking  back,  earnestly  besought  him  to 
hold  his  hand  a  little  while,  that  he  might  not  leave  what  he  was 
at  work  upon  inconclusive  and  imperfect;  but  the  soldier,  nothing 
moved  by  his  entreaty,  instantly  killed  him.  Others  again  relate, 
that  as  Archimedes  was  carrying  to  Marcellus  mathematical  instru- 
ments, dials,  spheres,  and  angles,  by  which  the  magnitude  of  the  sun 
might  be  measured  to  the  sight,  some  soldiers  seeing  him,  and  think- 
ing that  he  carried  gold  in  a  vessel,  slew  him.  Certain  it  is,  that  his 
death  was  very  afflicting  to  Marcellus ;  and  that  Marcellus  ever  after 
regarded  him  that  killed  him  as  a  murderer ;  and  that  he  sought  for 
his  kindred  and  honored  them  with  signal  favours.  —  Plutarch. 

The  known  works  of  Archimedes  include  the  following :  two 
books  on  the  Equilibrium  of  Planes,  with  an  interpolated  treatise 


GREEK  SCIENCE   IN  ALEXANDRIA  97 

on  the  Quadrature  of  the  Parabola,  two  books  on  the  Sphere 
and  the  Cylinder,  the  Circle  Measurement,  the  Spirals,  the  book 
of  Conoids  and  Spheroids,  the  Sand  Number,  two  books  on 
Floating  Bodies,  Choices.  Unlike  Euclid's  Elements,  these  are 
for  the  most  part  original  papers  on  new  mathematical  discoveries, 
which  were  also  often  communicated  to  his  contemporaries  in  the 
form  of  letters.  Pappus  quotes  Geminus  as  saying  of  Archimedes : 
"He  is  the  only  man  who  has  known  how  to  apply  to  all  things 
his  varied  natural  gifts  and  inventive  genius." 

ARCHIMEDES  AND  EUCLID.  —  In  contrasting  the  limitations  of 
Euclid's  Elements  with  the  broad  range  of  Greek  mathematics, 
Klein  characterizes  the  work  of  Archimedes  somewhat  as  follows : 

(1)  Quite  in  contrast  to  the  spirit  controlling  Euclid's  Elements, 
Archimedes  has  a  strongly  developed  sense  for  numerical  com- 
putation.    One  of  his  greatest  achievements  indeed  is  the  calcu- 
lation of  the  ratio  IT  of  the  circumference  of  a  circle  to  its  diameter, 
by  approximations  with  regular  polygons.     There  is  no  trace  of 
interest  for  such  numerical  results  with  Euclid,  who  merely  men- 
tions that  the  areas  of  two  circles  are  proportional  to  the  squares 
of  the  radii,  two  circumferences  as  the  radii,  regardless  of  the 
actual  proportionality  factor. 

(2)  A  far-reaching  interest  in  applications  of  all  sorts  is  char- 
acteristic of  Archimedes,  including  the  most  varied  physical  and 
technical  problems.     Thus  he  discovered  the  principles  of  hydro- 
statics and  constructed  engines  of  war.     Euclid  on  the  contrary 
does  not  even  mention  ruler  or  compass,  merely  postulating  that 
a  straight  line  can  be  drawn  through  two  points,  or  a  circle  de- 
scribed about  a  point.     Euclid  shares  the  view  of  certain  ancient 
schools  of  philosophy,  —  a  view  unfortunately  extant  in  certain 
quarters, — that  the  practical  application  of  a  science  is  something 
mechanical  and  unworthy.    The  very  greatest  mathematicians, 
Archimedes,  Newton,  Gauss,  have  combined  theory  and  applica- 
tions consistently.1 

1  Plutarch,  however,  says  :  "Archimedes  possessed  so  high  a  spirit,  so  profound 
a  soul,  and  such  treasures  of  highly  scientific  knowledge,  that  though  these  inven- 
tions (used  to  defend  Syracuse  against  the  Romans)  had  now  obtained  him  the  re- 
H 


98  A  SHORT  HISTORY  OF  SCIENCE 

(3)  Finally,  Archimedes  was  a  great  investigator  and  pioneer, 
who  in  each  of  his  works  carries  knowledge  a  step  forward.  This 
affects  materially  the  form  of  presentation.  In  a  most  recently 
discovered  manuscript,  the  procedure  is  essentially  modern  as 
contrasted  with  the  rigid  formalism  of  the  Elements. 

CIRCLE  MEASUREMENT.  —  In  this  Archimedes  proves  three 
theorems. 

(1)  Every  circle  is  equivalent  to  a  right  triangle  having  the 
sides  adjacent  to  the  right  angle  equal  respectively  to  the  radius 
and  circumference  of  the  circle. 

(2)  The  circle  has  to  the  square  on  its  diameter  approximately 
the  ratio  11:14. 

(3)  The  circumference  of  any  circle  is  three  times  as  great  as  the 
diameter  and  somewhat  more,  namely  less  than  f  but  more  than  ^. 

He  proves  the  first  theorem  by  showing  that  the  assumption 
that  the  circle  is  either  larger  or  smaller  than  the  triangle  leads  to 
a  contradiction.  The  second  he  bases  on  the  third,  at  which  he 
arrives  by  computing  successively  the  perimeters  of  both  inscribed 
and  circumscribed  polygons  of  3,  6,  12,  24,  48  and  96  sides.  All 
this  is  contrary  to  the  spirit  of  Euclid  and  essentially  modern  in 
its  method  of  successive  approximation.  The  difficulty  of  the 
achievement  in  view  of  the  imperfect  arithmetical  notation  avail- 
able can  hardly  be  overrated. 

QUADRATURE  OF  THE  PARABOLA.  —  Of  special  interest  is  his 
quadrature  of  the  parabola.  A  segment  is  formed  by  drawing  any 
chord  PQ  of  the  parabola  :  it  is  known  that  if  a  line  is  drawn  from 
the  middle  point  R  of  the  chord  parallel  to  the  axis  of  the  parabola, 
the  tangent  at  the  point  S  where  this  line  meets  the  curve  will  be 
parallel  to  the  chord,  and  the  perpendicular  from  S  to  the  chord 
is  greater  than  any  other  which  can  be  drawn  from  a  point  of  the 

nown  of  more  than  human  sagacity ;  he  yet  would  not  deign  to  leave  behind  him 
any  commentary  or  writing  on  such  subjects  ;  but,  repudiating  as  sordid  and  ignoble 
the  whole  trade  of  engineering,  and  every  sort  of  art  that  lends  itself  to  mere  use 
and  profit,  he  placed  his  whole  affection  and  ambition  in  those  purer  speculations 
where  there  can  be  no  reference  to  the  vulgar  needs  of  life ;  studies,  the  superiority 
of  which  to  all  others  is  unquestioned,  and  in  which  the  only  doubt  can  be  whether 
the  beauty  and  grandeur  of  the  subjects  examined,  or  the  precision  and  cogency  of 
the  methods  and  means  of  proof,  most  deserve  our  admiration." 


GREEK  SCIENCE  IN  ALEXANDRIA  99 

arc.  The  triangle  formed  by  joining  the  same  point  S  to  the  ends 
of  the  original  chord  being  wholly  contained  within  the  segment, 
the  area  of  the  latter  will  be  greater  than  that  of  the  triangle  and 
less  than  that  of  a  parallelogram  having  the  same  base  and  alti- 
tude. Now  the  segment  exceeds  the  triangle 
by  two  smaller  segments,  in  each  of  which 
triangles  STQ  and  SPU  are  again  inscribed. 
It  is  a  known  property  of  the  parabola  that 
each  of  these  triangles  has  one-eighth  the  area 
of  the  triangle  PSQ.  The  area  of  each  of  the 
two  smaller  segments  is  therefore  greater  than 
one-eighth  and  less  than  one-fourth  that  of  the  triangle  PSQ. 
The  area  of  the  original  segment  therefore  is  less  than  three-halves 
and  greater  than  five-fourths  that  of  triangle  PSQ.  The  construc- 
tion may  evidently  be  repeated  any  number  of  times,  and  the 
ratio  of  the  segment  to  the  triangle  will  lie  between  numbers  which 
converge  towards  four-thirds.  Archimedes  also  succeeded  in 
determining  the  area  of  the  ellipse. 

SPIRALS.  —  The  discussion  of  spirals  is  based  on  the  definition, 
"If  a  straight  line  moves  with  uniform  velocity  in  a  plane  about 
one  of  its  extremities  which  remains  fixed,  until  it  returns  to  its 
original  position,  and  if  at  the  same  time  a  point  moves  with  uni- 
form velocity  starting  at  the  fixed  point,  the  moving  point  de- 
scribes a  spiral."  With  the  simple  resources  at  his  command, 
he  also  succeeds  in  obtaining  the  quadrature  of  this  spiral,  and  in 
drawing  a  tangent  at  any  point.  In  these  quadratures  he  approx- 
imates the  summation  principle  of  the  modern  integral  calculus. 

Supplementing  Euclid's  treatment  of  the  regular  polyhedrons, 
Archimedes  investigates  the  semi-regular  solids  formed  by  com- 
bining regular  polygons  of  more  than  one  kind.  Of  these  he  finds 
13,  ten  of  which  have  two  kinds  of  bounding  polygons,  the  others 
three  kinds. 

SPHERE  AND  CYLINDER.  —  In  his  important  treatise  on  "  The 
Sphere  and  the  Cylinder"  he  derives  three  new  theorems : 

(1)  That  the  surface  of  a  sphere  is  four  times  the  area  of  its 
great  circle. 


100  A  SHORT  HISTORY  OF  SCIENCE 

(2)  That  the  convex  surface  of  a  segment  of  a  sphere  is  equal 
to  the  area  of  a  circle  whose  radius  is  equal  to  the  straight  line 
from  the  vertex  of  the  segment  to  any  point  in  the  perimeter  of 
its  base. 

(3)  That  the  cylinder  having  a  great  circle  of  the  sphere  for  its 
base  and  the  diameter  of  the  sphere  for  its  altitude  exceeds  the 
sphere  by  one-half,  both  in  volume  and  in  surface.     It  was  the 
figure  for  this  last  proposition  which  was  at  his  wish  carved  upon 
his  tombstone. 

In  attempting  to  solve  the  problem  of  passing  a  plane 
through  a  sphere  so  that  the  segments  thus  formed  shall  have 
either  their  surfaces  or  their  volumes  in  an  assigned  ratio,  he  is 
led  to  a  cubic  equation ;  he  appears  to  have  given  both  a  solution 
and  a  criterion  for  the  existence  of  a  positive  root,  but  the  work 
is  lost. 

In  his  Conoids  and  Spheroids  he  deals  with  the  bodies  formed 
by  the  revolution  of  the  ellipse,  parabola,  and  hyperbola,  by  means 
of  plane  cross-sections,  ascertains  the  volume  of  these  solids  by 
comparing  the  portion  between  two  neighboring  planes  with  an 
inscribed  and  a  circumscribed  cylinder,  —  much  in  the  modern 
manner. 

It  is  not  possible  to  find  in  all  geometry  more  difficult  and  more 
intricate  questions  or  more  simple  and  lucid  explanations  (than  those 
given  by  Archimedes).  Some  ascribe  this  to  his  natural  genius; 
while  others  think  that  incredible  effort  and  toil  produced  these,  to 
all  appearance,  easy  and  unlabored  results.  No  amount  of  inves- 
tigation of  yours  would  succeed  in  attaining  the  proof,  and  yet,  once 
seen,  you  immediately  believe  you  would  have  discovered  it;  by  so 
smooth  and  so  rapid  a  path  he  leads  you  to  the  conclusion  required. 

—  Plutarch. 

In  other  branches  of  mathematical  science  than  geometry  the 
work  of  Archimedes  was  relatively  even  more  important. 

The  so-called  Cattle  Problem,  for  example,  is  a  notable  per- 
formance in  the  algebra  of  linear  equations. 

"  The  sun  had  a  herd  of  bulls  and  cows,  all  of  which  were  either 


GREEK  SCIENCE  IN  ALEXANDRIA'- ;  ; : . :    101 


white,  gray,  dun,  or  piebald;  the  number  of  piebald  bulls  was 
less  than  the  number  of  white  bulls  by  (J  +  f  )  of  the  number  of 
gray  bulls,  it  was  less  than  the  number  of  gray  bulls  by  (J  +  J) 
of  the  number  of  dun  bulls,  and  it  was  less  than  the  number  of 
dun  bulls  by  (£  +  y)  of  the  number  of  white  bulls.  The  number 
of  white  cows  was  d  +  |)  of  the  number  of  gray  cattle  (bulls  and 
cows),  the  number  of  gray  cows  was  (i  +  i)  of  the  number  of 
dun  cattle,  the  number  of  dun  cows  was  (3-  +  i)  of  the  number  of 
piebald  cattle,  and  the  number  of  piebald  cows  was  (i  +  y)  of  the 
number  of  white  cattle."  The  seven  equations  are  insufficient  to 
determine  the  eight  unknown  quantities.  The  solution  attributed 
to  Archimedes  consists  of  numbers  of  nine  figures  each.  j  ^ 

Again  he  succeeds  in  summing  the  series  of  squares  :  1,  4,  9,  16*, 
25,  36,  etc.,  to  n  terms,  expressing  the  result  in  geometrical  form. 
Both  proof  and  formulation  are  of  course  much  more  complicated 
by  reason  of  the  entire  lack  of  an  algebraic  symbolism,  the  same 
remark  naturally  applying  also  to  the  preceding  cattle  problem 
and  to  the  cubic  equation  referred  to  above.  This  last  was  in- 
deed to  Archimedes  not  primarily  an  equation  at  all,  but  a  pro- 
portion 

a-x:b::%a?:x2. 

In  his  Circle  Measurement  already  outlined,  he  showed  mastery 
of  square  root,  and  the  comparison  of  irrational  numbers  with 
fractions,  showing  for  example  that 


How  these  fractions  were  obtained  cannot  be  certainly  deter- 
mined, but  it  was  presumably  by  a  process  analogous  at  least  to 
the  modern  method  of  continued  fractions,  though  such  fractions 
themselves  could  not  have  been  known  to  him. 

In  the  Sand  Counting,  Archimedes  undertakes  to  give  a  number 
which  shall  exceed  the  number  of  grains  of  sand  in  a  sphere  with  a 
radius  equal  to  the  distance  from  the  earth  to  the  starry  firma- 
ment. The  treatise  begins  :  "  Many  people  believe,  King  Gelon, 
that  the  number  of  sand  grains  is  infinite.  I  mean  not  the  sand 


102  A   SHORT  HISTORY  OF  SCIENCE 

about  Syracuse,  nor  even  that  in  Sicily,  but  also  that  on  the  whole 
mainland,  inhabited  and  uninhabited.  There  are  others  again 
who  do  not  indeed  assume  this  number  to  be  infinite,  but  so  great 
that  no  number  is  ever  named  which  exceeds  this.  ...  I  will 
attempt  to  show  however  by  geometrical  proofs  which  you  will 
accept  that  among  the  numbers  which  I  have  named  .  .  .  some 
not  only  exceed  the  number  of  a  sand-heap  of  the  size  of  the  earth, 
but  also  of  that  of  a  pile  of  the  size  of  the  universe."  He  assumes 
that  10,000  grains  of  sand  would  make  the  size  of  a  poppy-seed, 
that  the  diameter  of  a  poppy-seed  is  not  less  than  one-fortieth  of  a 
finger-breadth,  that  the  diameter  of  the  earth  is  less  than  a  million 
stadia,  that  the  diameter  of  the  universe  is  less  than  10,000  di- 
ameters of  the  earth.  To  express  the  vast  number  which  results 
.from  these  assumptions  — 1063  in  our  notation  —  he  employs 
an  ingenious  system  of  units  of  higher  order  comparable  with  the 
modern  use  of  exponents,  an  immense  advance  on  current  arith- 
metical symbolism. 

MECHANICS  OF  ARCHIMEDES.  —  In  mechanics  Archimedes  is 
a  pioneer,  giving  the  first  mathematical  proofs  known.  In  two 
books  on  Equiponderance  of  Planes  or  Centres  of  Plane  Gravities, 
he  deals  with  the  problem  of  determining  the  centres  of  gravity 
of  a  variety  of  plane  figures,  including  the  parabolic  segment. 
A  treatise  on  levers  and  perhaps  on  machines  in  general  has  been 
lost,  as  also  a  work  on  the  construction  of  a  celestial  sphere.  A 
sphere  of  the  stars  and  an  orrery  constructed  by  him  were  long 
preserved  at  Rome.  He  describes  an  original  apparatus  for  deter- 
mining the  angular  diameter  of  the  sun,  discussing  its  degree  of 
accuracy. 

The  lever  and  the  wedge  had  been  practically  known  from 
remote  antiquity,  and  Aristotle  had  discussed  the  practice  of 
dishonest  tradesmen  shifting  the  fulcrum  of  scales  towards  the 
pan  in  which  the  weights  lay,  but  no  previous  attempt  at  exact 
mathematical  treatment  is  known. 

Archimedes  assumes  as  evident  at  the  outset : 

(1)  Magnitudes  of  equal  weight  acting  at  equal  distances  from 
their  point  of  support  are  in  equilibrium ; 


GREEK  SCIENCE   IN  ALEXANDRIA  ^i#3 

(2)  Magnitudes  of  equal  weight  actings +p#ileqfial  distances 
from  their  point  of  support  aR?.  not  in  equilibrium,  but  the  one 
acting  at  the  greater  distance  sinks. 

From  these  he  deduces : 

(3)  Commensurable  magnitudes  are  in  equilibrium  when  they 
are  inversely  proportional  to  their  distances  from  the  point  of 
support. 

In  a  work  on  Floating  Bodies,  extant  in  a  Latin  version  by 
Tartaglia,  Archimedes  defines  a  fluid  as  follows :  "  Let  it  be 
assumed  that  the  nature  of  a  fluid  is  such  that,  all  its  parts  lying 
evenly  and  continuous  with  one  another,  the  part  subject  to  less 
pressure  is  expelled  by  the  part  subject  to  greater  pressure.  But 
each  part  is  pressed  perpendicularly  by  the  fluid  above  it,  if  the 
fluid  is  falling  or  under  any  pressure."  "  Every  solid  body  lighter 
than  a  liquid  in  which  it  floats  sinks  so  deep  that  the  mass  of  liquid 
which  has  the  same  volume  with  the  submerged  part  weighs  just 
as  much  as  the  floating  body."  The  specific  gravity  of  heavier 
bodies  was  of  course  employed  in  his  solution  of  the  crown  problem, 
which  with  his  achievements  as  a  military  engineer  gave  him  a 
great  reputation  among  his  contemporaries.  Vitruvius  in  his 
De  Architectures  says: 

Though  Archimedes  discovered  many  curious  matters  that 
evinced  great  intelligence,  that  which  I  am  about  to  mention  is  the 
most  extraordinary.  Hiero,  when  he  obtained  the  regal  power  in 
Syracuse,  having,  on  the  fortunate  turn  of  his  affairs,  decreed  a  votive 
crown  of  gold  to  be  placed  in  a  certain  temple  to  the  immortal  gods, 
commanded  it  to  be  made  of  great  value,  and  assigned  for  this  purpose 
an  appropriate  weight  of  the  metal  to  the  manufacturer.  The  latter, 
in  due  time,  presented  the  work  to  the  king,  beautifully  wrought; 
and  the  weight  appeared  to  correspond  with  that  of  the  gold  which 
had  been  assigned  for  it. 

But  a  report  having  been  circulated,  that  some  of  the  gold  had 
been  abstracted,  and  that  the  deficiency  thus  caused  had  been  sup- 
plied by  silver,  Hiero  was  indignant  at  the  fraud,  and,  unacquainted 
with  the  method  by  which  the  theft  might  be  detected,  requested 
Archimedes  would  undertake  to  give  it  his  attention.  Charged  with 


104  A  SHORT  HISTORY  OF  SCIENCE 

this  commisste>  v  b^hv^chance  went  to  a  bath,  and  on  jumping  into 
the  tub,  perceived  that,  just  in  the  proportion  that  his  body  became 
immersed,  in  the  same  proportion  the  water  ran  out  of  the  vessel. 
Whence,  catching  at  the  method  to  be  adopted  for  the  solution  of  the 
proposition,  he  immediately  followed  it  up,  leapt  out  of  the  vessel  in 
joy,  and  returning  home  naked,  cried  out  with  a  loud  voice  that  he 
had  found  that  of  which  he  was  in  search,  for  he  continued  exclaiming, 
'  I  have  found  it,  I  have  found  it ! '  —  Vitruvius. 

Archimedes,  who  combined  a  genius  for  mathematics  with  a  physical 
insight,  must  rank  with  Newton,  who  lived  nearly  two  thousand 
years  later,  as  one  of  the  founders  of  mathematical  physics.  .  .  .  The 
day  (when  having  discovered  his  famous  principle  of  hydrostatics 
he  ran  through  the  streets  shouting  Eureka  !  Eureka !)  ought  to  be 
celebrated  as  the  birthday  of  mathematical  physics ;  the  science  came 
of  age  when  Newton  sat  in  his  orchard.  —  Whitehead. 

The  recently  discovered  New  Manuscript l  of  Archimedes 
throws  a  very  interesting  light  on  his  methods  of  attacking  prob- 
lems in  mechanics,  as  well  as  on  his  use  of  mechanical  methods 
for  geometrical  problems.  Naturally  his  mathematical  methods 
are  highly  developed  in  comparison  with  the  relatively  simple 
problems  of  mechanics  with  which  he  deals. 

'  Certain  things  first  became  clear  to  me  by  a  mechanical  method, 
although  they  had  to  be  demonstrated  by  geometry  afterwards  because 
their  investigation  by  the  said  method  did  not  furnish  an  actual 
demonstration.  But  it  is  of  course  easier,  when  we  have  previously 
acquired,  by  the  method,  some  knowledge  of  the  questions,  to  supply 
the  proof  than  it  is  to  find  it  without  any  previous  knowledge.  I 
apprehend  that  some,  either  of  my  contemporaries  or  of  my  succes- 
sors, will,  by  means  of  the  method  when  once  established,  be  able  to 
discover  other  theorems  .  .  .  which  have  not  yet  occurred  to  me.' 

Our  admiration  of  the  genius  of  the  greatest  mathematician  of 
antiquity  must  surely  be  increased,  if  that  were  possible,  by  a  perusal 
of  the  work  before  us.  —  Heath. 

AKCHIMEDES  AS  AN  ENGINEER.  —  His  engineering  skill,  which 
has  gained  from  an  eminent  German  historian  the  appellation  of 

1  See  Reviews  by  C.  S.  Slichter  and  D.  E.  Smith.  Bulletin,  American  Mathe- 
matical Society,  May,  1908,  Feb.  1913. 


GREEK  SCIENCE  IN  ALEXANDRIA  105 

"the  technical  Yankee  of  antiquity/'  may  be  inferred  from  Plu- 
tarch's account  of  the  siege  of  Syracuse :  — 

Now  the  Syracusans,  seeing  themselves  assaulted  by  the  Romans, 
both  by  sea  and  by  land,  were  marvellously  perplexed,  and  could  not 
tell  what  to  say,  they  were  so  afraid ;  imagining  it  was  impossible  for 
them  to  withstand  so  great  an  army.  But  when  Archimedes  fell  to 
handling  his  engines,  and  set  them  at  liberty,  there  flew  in  the  air 
infinite  kinds  of  shot,  and  marvellous  great  stones,  with  an  incredible 
noise  and  force  on  the  sudden,  upon  the  footmen  that  came  to  assault 
the  city  by  land,  bearing  down,  and  tearing  in  pieces  all  those  which 
came  against  them,  or  in  what  place  soever  they  lighted,  no  earthly 
body  being  able  to  resist  the  violence  of  so  heavy  a  weight ;  so  that 
all  their  ranks  were  marvellously  disordered.  And  as  for  the  galleys 
that  gave  assault  by  sea,  some  were  sunk  with  long  pieces  of  timber 
like  unto  the  yards  of  ships,  whereto  they  fasten  their  sails,  which 
were  suddenly  blown  over  the  walls  with  force  of  their  engines  into 
their  galleys,  and  so  sunk  them  by  their  over  great  weight. 

These  machines  (used  in  the  defense  of  the  Syracusans  against 
the  Romans  under  Marcellus)  he  (Archimedes)  had  designed  and 
contrived,  not  as  matters  of  any  importance,  but  as  mere  amusements 
in  geometry;  in  compliance  with  king  Hiero's  desire  and  request, 
some  time  before,  that  he  should  reduce  to  practice  some  part  of  his 
admirable  speculation  in  science,  and  by  accommodating  the  theo- 
retic truth  to  sensation  and  ordinary  use,  bring  it  more  within  the 
appreciation  of  people  in  general.  Eudoxus  and  Archytas  had  been 
the  first  originators  of  this  far-famed  and  highly-prized  art  of  me- 
chanics, which  they  employed  as  an  elegant  illustration  of  geometrical 
truths,  and  as  means  of  sustaining  experimentally,  to  the  satisfaction 
of  the  senses,  conclusions  too  intricate  for  proof  by  words  and  dia- 
grams. As,  for  example,  to  solve  the  problem,  so  often  required  in 
constructing  geometrical  figures,  given  the  two  extremes,  to  find  the 
two  mean  lines  of  a  proportion,  both  these  mathematicians  had  re- 
course to  the  aid  of  instruments,  adapting  to  their  purpose  certain 
curves  and  sections  of  lines.  But  what  with  Plato's  indignation  at 
it,  and  his  invectives  against  it  as  the  mere  corruption  and  annihila- 
tion of  the  one  good  of  geometry,  —  which  was  thus  shamefully  turn- 
ing its  back  upon  the  unembodied  objects  of  pure  intelligence  to  recur 
to  sensation,  and  to  ask  help  (not  to  be  obtained  without  base  super- 


106  A  SHORT  HISTORY  OF  SCIENCE 

visions  and  depravation)  from  matter ;  so  it  was  that  mechanics  came 
to  be  separated  from  geometry,  and,  repudiated  and  neglected  by 
philosophers,  took  its  place  as  a  military  art. 

One  of  his  most  famous  inventions  was  the  water-screw  used 
for  irrigation,  in  Egypt,  and  for  pumping.  On  occasion  of  diffi- 
culty in  the  launching  of  a  certain  ship  he  successfully  applied 
a  cogwheel  apparatus  with  an  endless  screw. 

Archimedes  .  .  .  had  stated  that  given  the  force,  any  given 
weight  might  be  moved,  and  even  boasted,  we  are  told,  relying  on 
the  strength  of  demonstration,  that  if  there  were  another  earth,  by 
going  into  it  he  could  remove  this.  Hiero  being  struck  with  amaze- 
ment at  this,  and  entreating  him  to  make  good  this  problem  by  actual 
experiment,  and  show  some  great  weight  moved  by  a  small  engine, 
he  fixed  accordingly  upon  a  ship  of  burden  out  of  the  king's  arsenal, 
which  could  not  be  drawn  out  of  the  dock  without  great  labor  and 
many  men ;  and,  loading  her  with  many  passengers  and  a  full  freight, 
sitting  himself  the  while  far  off  with  no  great  endeavor,  but  only 
holding  the  head  of  the  pulley  in  his  hand  and  drawing  the  cords  by 
degrees,  he  drew  the  ship  in  a  straight  line,  as  smoothly  and  evenly, 
as  if  she  had  been  in  the  sea.  The  king,  astonished  at  this,  and  con- 
vinced of  the  power  of  the  art,  prevailed  upon  Archimedes  to  make 
him  engines  accommodated  to  all  the  purposes,  offensive  and  defensive, 
of  a  siege  .  .  .  the  apparatus  was,  in  most  opportune  time,  ready  at 
hand  for  the  Syracusans,  and  with  it  also  the  engineer  himself. 

—  Plutarch. 

In  astronomy  his  orrery  has  been  mentioned ;  he  also  attempted 
to  determine  the  length  of  the  year  more  closely. 

To  the  critical  estimates  already  cited  may  be  added  as  typical 
of  countless  others :  — 

Whoever  gets  to  the  bottom  of  the  works  of  Archimedes  will 
admire  the  discoveries  of  the  moderns  less.  —  Leibnitz. 

His  discoveries  are  forever  memorable  for  their  novelty  and  the 
difficulty  which  they  presented  at  that  time,  and  because  they  are 
the  germ  of  a  great  part  of  those  which  have  since  been  made,  chiefly 
in  all  branches  of  geometry  which  have  for  their  object  the  measure- 


GREEK  SCIENCE   IN  ALEXANDRIA  107 

ment  of  the  dimensions  of  lines  and  curved  surfaces  and  which  require 
the  consideration  of  the  infinite.  —  Mack. 

The  genius  of  Archimedes  created  the  theory  of  the  composition 
of  parallel  forces,  of  centres  of  gravity,  and  of  equilibrium  of  float- 
ing bodies.  But  antiquity  went  no  farther;  not  only  were  the  first 
principles  of  dynamics  unsuspected,  but  the  statistical  composition  of 
concurrent  forces  was  unknown,  and  the  explanation  of  machines 
was  confined  to  extension  of  the  principles  of  the  lever,  which  is  the 
starting-point  of  the  works  of  Archimedes,  but  may  nevertheless 
have  been  recognized  before  him.  —  Tannery. 

ALEXANDRIAN  GEOGRAPHY  :  EARTH  MEASUREMENT.  —  The  far 
reaching  conquests  of  Alexander  and  the  resulting  migrations  and 
colonizations  naturally  gave  a  powerful  stimulus  to  geography 
as  a  branch  of  descriptive  knowledge.  Chaldean  records  became 
accessible  to  the  Alexandrian  Greeks  and  a  more  accurate  system 
of  time-measurement  was  introduced.  Until  about  this  period 
it  had  been  customary  to  make  appointments  at  the  time  when 
a  person's  shadow  should  have  a  certain  length. 

ERATOSTHENES,  —  275-194  B.C.,  librarian  of  the  great  library  at 
Alexandria,  making  a  systematic  quantitative  study  of  the  data 
thus  collected,  laid  the  foundations  of  mathematical  geography — 
a  transformation  quite  analogous  to  that  taking  place  in  as- 
tronomy. After  a  historical  review  he  gives  numerical  data  about 
the  inhabited  earth,  which  he  estimates  to  have  a  length  of  78,000 
stadia  and  a  breadth  of  38,000.  In  connection  with  this  he  gives 
also  a  remarkably  successful  determination  of  the  circumference 
of  the  earth.  This  was  based  on  his  observation  that  a  gnomon  at 
Syene  (Assouan)  threw  no  shadow  at  noon  of  the  summer  solstice, 
while  at  Alexandria  the  zenith  distance  of  the  sun  at  noon  was 
^y  of  the  circumference  of  the  heavens.  Assuming  the  two  places 
to  lie  on  the  same  meridian  and  taking  their  distance  apart  as 
5000  stadia,  he  infers  that  the  whole  circumference  must  be  250,000 
stadia.  He  or  some  successor  afterwards  substituted  252,000, 
perhaps  in  order  to  obtain  a  round  number,  700  stadia,  for  the 
length  of  one  degree. 

This  result,  subject  to  some  uncertainty  as  to  the  length  of 


108  A  SHORT  HISTORY  OF  SCIENCE 

the  stadium,  was  a  close  approximation  to  the  real  circumference, 
but  we  may  suppose  that  this  degree  of  accuracy  was  to  some 
extent  a  matter  of  accident.  Posidonius,  a  noted  Stoic  philosopher, 
born  in  136  B.C.,  stated  that  the  bright  star  Canopus  culminated 
just  on  the  horizon  at  Rhodes,  while  its  meridian  altitude  at 
Alexandria  was  "  a  quarter  of  a  sign,  that  is,  one  forty-eighth  part 
of  the  zodiac."  This  would  correspond  with  a  circumference  of 
240,000  stadia,  the  method  being  quite  inferior  in  accuracy  to  that 
of  Eratosthenes,  on  account  of  the  impossibility  of  determining 
when  a  star  is  just  on  the  horizon.  Eratosthenes  is  also  credited 
with  measuring  the  obliquity  of  the  ecliptic  with  an  error  of  but 
about  seven  minutes. 

A  student  of  the  Athenian  Platonists  and  a  man  of  extraor- 
dinary versatility,  philosopher,  philologian,  mathematician,  ath- 
lete, Eratosthenes  wrote  on  many  subjects.  He  may  well  have 
been  responsible  for  the  introduction  of  leap-year  into  the  Egyp- 
tian calendar  by  the  "  Decree  of  Canopus  "  in  238  B.C., 

in  order  that  the  seasons  may  continually  render  their  service  accord- 
ing to  the  present  order  and  that  it  may  not  happen  that  some  of 
the  public  festivals  which  are  celebrated  in  the  winter  come  to  be 
observed  sometimes  in  the  summer.  .  .  . 

He  invented  a  method  and  a  mechanical  apparatus  for  duplicat- 
ing the  cube.1  Such  a  mechanical  solution  is  naturally  obnoxious 
to  the  principles  of  Plato  and  Euclid. 

His  so-called  "sieve"  is  a  method  for  systematically  separating 
out  the  prime  numbers  by  arranging  all  the  natural  numbers 
in  order,  and  then  striking  out  first  all  multiples  of  2,  then  of  3, 
and  so  forth,  thus  sifting  out  all  but  the  primes  1,  2,  3,  5,  7,  11, 
13,  17,  etc. 

APOLLONIUS  OF  PERGA,  about  260-200  B.C.,  "the  great  geom- 
eter," was  the  last  of  this  famous  Alexandrian  group  of  mathema- 
ticians, and  owes  his  reputation  to  his  important  work  on  the  conic 
sections.  His  predecessors  had  in  general  recognized  only  those  sec- 
tions formed  from  right  circular  cones  by  planes  normal  to  an  ele- 

1  See  Gow,  p.  245. 


GREEK  SCIENCE   IN   ALEXANDRIA  109 

ment.  Archimedes,  indeed,  and  Euclid  obtained  ellipses  by  passing 
other  planes  through  right  cones,  but  Apollonius  first  showed  that 
any  cone  and  any  section  could  be  taken,  and  introduced  the 
names  ellipse,  parabola,  and  hyperbola.  In  the  prefatory  letter  to 
Book  I,  Apollonius  says  to  the  friend  to  whom  it  is  addressed :  — 

'Apollonius  to  Eudemus,  greeting.  When  I  was  in  Pergamum 
with  you,  I  noticed  that  you  were  eager  to  become  acquainted  with 
my  Conies ;  so  I  send  you  now  the  first  book  with  corrections  and  will 
forward  the  rest  when  I  have  leisure.  I  suppose  you  have  not  for- 
gotten that  I  told  you  that  I  undertook  these  investigations  at  the 
request  of  Naucrates  the  geometer,  when  he  came  to  Alexandria  and 
stayed  with  me;  and  that,  having  arranged  them  in  eight  books,  I 
let  him  have  them  at  once,  not  correcting  them  very  carefully  (for 
he  was  on  the  point  of  sailing)  but  setting  down  everything  that 
occurred  to  me,  with  the  intention  of  returning  to  them  later.  Where- 
fore I  now  take  the  opportunity  of  publishing  the  needful  emendations. 
But  since  it  has  happened  that  other  people  have  obtained  the  first 
and  second  books  of  my  collections  before  correction,  do  not  wonder 
if  you  meet  with  copies  which  are  different  from  this.'  —  Gow. 

Of  the  eight  books,  the  first  four  are  devoted  to  an  elementary 
introduction.  In  Book  I  he  defines  the  cone  as  generated  by  a 
straight  line  passing  through  a  point  on  the  circumference  of  a 
circle  and  a  fixed  point  not  in  the  same  plane ;  he  fixes  the  manner 
in  which  sections  are  to  be  taken  and  defines  diameters  and  ver- 
tices of  the  curves,  also  the  latus  rectum  and  centre,  conjugate 
diameters  and  axes.  The  other  branch  of  the  hyperbola  is  taken 
due  account  of  for  the  first  time.  In  Book  II  asymptotes  are 
defined  by  the  statement :  "  One  draws  a  tangent  at  a  point  of  the 
hyperbola,  measures  on  it  the  length  of  the  diameter  parallel  to  it, 
and  connects  the  point  thus  determined  with  the  centre  of  the 
hyperbola."  Book  III  contains  numerous  theorems  on  tangents 
and  secants  and  introduces  foci  with  the  definition :  "  A  focus  is 
a  point  which  divides  the  major  axis  into  two  parts  whose  rectangle 
is  one-fourth  that  of  the  latus  rectum  and  the  major  axis,"  or  the 
square  on  the  minor  axis.  The  focus  of  the  parabola  however  is 
not  recognized,  nor  has  he  any  knowledge  of  the  directrix  of  a 


110  A  SHORT  HISTORY  OF  SCIENCE 

conic  section,  these  omissions  being  first  filled  by  Pappus  in  the 
third  century  A.D.  It  is  shown  that  the  normal  makes  equal  angles 
with  the  focal  radii  to  the  point  of  contact,  and  that  the  latter 
have  a  constant  sum  for  the  ellipse,  a  constant  difference  for  the 
hyperbola.  This  book,  he  says  in  the  letter  quoted  above,  "  contains 
many  curious  theorems,  most  of  them  are  pretty  and  new,  useful 
for  the  synthesis  of  solid  loci.  ...  In  the  invention  of  these,  I  ob- 
served that  Euclid  had  not  treated  synthetically  the  locus  .  .  f 
but  only  a  certain  small  portion  of  it,  and  that  not  happily,  nor  in- 
deed was  a  complete  treatise  possible  at  all  without  my  discoveries." 
These  three  books,  which  are  indeed  based  largely  on  the  earlier 
work  of  Euclid  and  others,  contain  most  of  the  properties  of  conic 
sections  discussed  in  modern  text-books  on  analytic  geometry. 
Book  IV  discusses  the  intersections  of  conies,  treating  tangency 
correctly  as  equivalent  to  two  ordinary  intersections.  In  Book  V 
Apollonius  even  undertakes  the  difficult  problem  of  determining 
the  longest  and  shortest  lines  which  can  be  drawn  from  a  given 
point  to  a  conic,  identifying  this  with  the  problem  of  drawing 
normals  from  a  given  point.  He  succeeds  in  discovering  the  points 
for  which  two  such  normals  coincide,  i.  e.  what  we  call  the  centre 
of  curvature.  Book  VI  deals  with  equal  and  similar  conies,  reach- 
ing the  problem  of  passing  through  a  given  cone  a  plane  which 
shall  cut  out  a  given  ellipse.  Book  VII  deals  with  conjugate 
diameters  and  the  complementary  chords  parallel  to  them.  Book 
VIII  is  lost.  On  the  whole,  in  this  remarkable  work  of  some  400 
propositions  he  achieved  nearly  all  the  results  which  are  included 
in  our  modern  elementary  analytic  geometry,  even  approximating 
the  introduction  of  a  system  of  coordinates  by  his  use  of  lines 
parallel  to  the  principal  axes. 

It  is  noteworthy  that  Fermat,  one  of  the  inventors  of  modern 
analytic  geometry,  was  led  to  it  by  attempting  to  restore  certain 
lost  proofs  of  Apollonius  on  loci. 

Of  his  other  mathematical  writings  little  more  than  the  titles 
are  known.  Among  these  are  one  on  burning  mirrors,  one  on 
stations  and  retrogressions  of  the  planets,  and  one  on  the  use  and 
theory  of  the  screw.  In  astronomy  he  is  believed  to  have  sug- 


GREEK  SCIENCE  IN  ALEXANDRIA  111 

gested  expressing  the  motions  of  the  planets  by  combining  uniform 
circular  motions,  an  idea  afterwards  elaborated  by  Hipparchus 
and  Ptolemy.  How  far  his  mathematical  results  were  new,  how 
far  he  merely  compiled  and  coordinated  the  work  of  others,  notably 
Euclid  and  Archimedes,  cannot  be  precisely  determined,  but  the 
proportion  of  original  work  is  certainly  very  large. 

On  the  arithmetical  side  he  obtained  a  closer  approximation 
than  Archimedes  for  the  value  of  IT,  invented  an  abridged  method 
of  multiplication,  and  employed  numbers  of  higher  order  in  the 
manner  of  Archimedes.  This  last  experiment  if  followed  out  to 
its  logical  conclusions  might  have  had  fundamental  significance 
for  the  future  development  of  computation.  In  the  words  of 
Gow:  — 

he,  as  well  as  Archimedes,  lost  the  chance  of  giving  to  the  world 
once  for  all  its  numerical  signs.  That  honor  was  reserved  by  the 
irony  of  fate  for  a  nameless  Indian  of  an  unknown  time,  and  we  know 
not  whom  to  thank  for  an  invention  which  has  been  as  important  as 
any  to  the  general  progress  of  intelligence. 

APOLLONIUS  AND  ARCHIMEDES.  —  With  Apollonius  and  Archi- 
medes the  ancient  mathematics  had  accomplished  whatever  was 
possible  without  the  resources  of  analytic  geometry  and  infinitesi- 
mal calculus,  which,  though  already  foreshadowed,  were  not  fully 
realized  until  the  seventeenth  century. 

It  is  not  only  a  decided  preference  for  synthesis  and  a  complete 
denial  of  general  methods  which  characterize  the  ancient  mathematics 
as  against  our  newer  science  (modern  mathematics) :  besides  this 
external  formal  difference  there  is  another  real,  more  deeply  seated, 
contrast,  which  arises  from  the  different  attitudes  which  the  two  as- 
sumed relative  to  the  use  of  the  concept  of  variability.  For  while  the 
ancients,  on  account  of  considerations  which  had  been  transmitted  to 
them  from  the  philosophic  school  of  the  Eleatics,  never  employed  the 
concept  of  motion,  the  spatial  expression  for  variability,  in  their 
rigorous  system,  and  made  incidental  use  of  it  only  in  the  treatment 
of  phoronomically  generated  curves,  modern  geometry  dates  from  the 
instant  that  Descartes  left  the  purely  algebraic  treatment  of  equations 


112  A  SHORT  HISTORY  OF  SCIENCE 

and  proceeded  to  investigate  the  variations  which  an  algebraic  ex- 
pression undergoes  when  one  of  its  variables  assumes  a  continuous 
succession  of  values.  —  Hankel. 

In  one  of  the  most  brilliant  passages  of  his  Aperqu  historique 
Chasles  remarks  that,  while  Archimedes  and  Apollonius  were  the 
most  able  geometricians  of  the  old  world,  their  works  are  distinguished 
by  a  contrast  which  runs  through  the  whole  subsequent  history  of 
geometry.  Archimedes,  in  attacking  the  problem  of  the  quadrature 
of  curvilinear  areas,  established  the  principles  of  the  geometry  which 
rests  on  measurements;  this  naturally  gave  rise  to  the  infinitesimal 
calculus,  and  in  fact  the  method  of  exhaustions  as  used  by  Archimedes 
does  not  differ  in  principle  from  the  method  of  limits  as  used  by 
Newton.  Apollonius,  on  the  other  hand,  in  investigating  the  proper- 
ties of  conic  sections  by  means  of  transversals  involving  the  ratio  of 
rectilineal  distances  and  of  perspective,  laid  the  foundations  of  the 
geometry  of  form  and  position.  — •  Ball. 

The  works  of  Archimedes  and  Apollonius  marked  the  most 
brilliant  epoch  of  ancient  geometry.  They  may  be  regarded,  more- 
over, as  the  origin  and  foundation  of  two  questions  which  have  occu- 
pied geometers  at  all  periods.  The  greater  part  of  their  works 
are  connected  with  these  and  are  divided  by  them  into  two  classes, 
so  that  they  seem  to  share  between  them  the  domain  of  geometry. 

The  first  of  these  two  great  questions  is  the  quadrature  of  curvi- 
linear figures,  which  gave  birth  to  the  calculus  of  the  infinite,  con- 
ceived and  brought  to  perfection  successively  by  Kepler,  Cavalieri, 
Fermat,  Leibnitz  and  Newton. 

The  second  is  the  theory  of  conic  sections,  for  which  were  in- 
vented first  the  geometrical  analysis  of  the  ancients,  afterwards 
the  methods  of  perspective  and  of  transversals.  This  was  the  pre- 
lude to  the  theory  of  geometrical  curves  of  all  degrees,  and  to  that 
considerable  portion  of  geometry  which  considers,  in  the  general 
properties  of  extension,  only  the  forms  and  situations  of  figures, 
and  uses  only  the  intersection  of  lines  or  surfaces  and  the  ratios  of 
rectilineal  distances. 

These  two  great  divisions  of  geometry,  which  have  each  its  pe- 
culiar character,  may  be  designated  by  the  names  of  Geometry  of 
Measurements  and  Geometry  of  Forms  and  Situations,  or  Geometry 
of  Archimedes  and  Geometry  of  Apollonius.  —  Chasles  (Gow). 


GREEK  SCIENCE   IN  ALEXANDRIA  113 

MEDICAL  SCIENCE  AT  ALEXANDRIA.  BEGINNINGS  OF  HUMAN 
ANATOMY.  —  Alexandria  is  famous  in  the  history  of  medicine  for 
many  reasons.  It  was  here  that  human, — as  contrasted  with  com- 
parative, —  anatomy  was  first  freely  studied  (probably  favored 
by  the  Egyptian  practice  of  disemboweling  and  embalming  the 
dead)  with  the  result  that  many  of  the  grotesque  errors  of  the 
earlier  Greeks,  including  even  Aristotle,  were  corrected.  In  this 
connection  two  names,  and  those  of  rivals,  have  come  down  to 
us  as  of  chief  importance,  Herophilus  and  Erasistratus.  The 
former,  himself  a  student  at  Cos,  was  a  close  follower  of  the  teach- 
ings of  Hippocrates  and  regarded  by  the  ancient  world  as  his 
worthy  successor.  Erasistratus,  on  the  contrary,  opposed  the 
Hippocratic  doctrines.  Both  became  distinguished  anatomists. 
It  is  believed  that  the  valves  of  the  heart  were  first  recognized 
and  named  by  Erasistratus,  who  also  studied  and  described 
the  divisions,  cavities  and  membranes  of  the  brain,  as  well 
as  the  true  origin  and  nature  of  the  nerves.  Herophilus  like- 
wise studied  the  brain,  the  pulmonary  artery  and  the  liver, 
besides  giving  to  the  duodenum  the  name  (twelve-inch) 
which  it  still  bears.  Physiology,  meanwhile,  made  little  or  ho 
progress,  and  Cicero,  two  centuries  later,  still  speaks  of  the 
arteries  as  "air  tubes."  It  appears  also  that  vivisection  as 
well  as  anatomy  was  practised  at  Alexandria,  and  probably 
even  upon  human  beings. 

Pergamtim,  in  Asia  Minor,  was  for  a  time  a  rival  centre  of 
medical  learning  and  medical  education,  but  was  eventually 
overshadowed  by  the  more  famous  Alexandrian  school.  Of  this 
last  the  most  celebrated  pupil  was  Galen  (born  130  A.D.),  the 
most  noted  medical  man  of  the  ancient  Roman  world.  Galen  was 
a  native  of  Pergamum  who,  having  first  studied  at  home  and  at 
Smyrna,  spent  some  years  at  Alexandria.  He  then  returned  to 
Pergamum,  but  soon  went  to  Rome,  where  he  became  physician 
to  the  Emperor  Commodus.  Galen  was  an  original  and  volu- 
minous writer  on  anatomy.  That  his  name  is  still  constantly 
linked  with  that  of  Hippocrates  is  probably  the  best  evidence  of 
his  importance  in  the  history  of  medical  science. 


114 


A  SHORT  HISTORY  OF  SCIENCE 


REFERENCES  FOR  READING 

BALL.     Chapter  IV  to  page  84. 

BERRY.     Chapter  II,  Articles  31-36. 

GARRISON,  F.  H.    History  of  Medicine  (On  Galen,  Herophilus,  Erasistratus, 

etc.). 

Gow.     Chapter  VII. 
HEATH,  T.  L.    Euclid's  Elements.     The  Works  of  Archimedes.    ApoUonius  of 

Perga. 

MACH,  E.     Science  of  Mechanics  (on  Archimedes). 
MAHAFFY,  J.    Alexander's  Empire. 


The  three  normals  to  the  ellipse.     Apollonius. 


CHAPTER  VI 
THE  DECLINE  OF  ALEXANDRIAN  SCIENCE 

The  century  which  produced  Euclid,  Archimedes  and  Apollonius 
was  .  .  .  the  time  at  which  Greek  mathematical  genius  attained  its 
highest  development.  For  many  centuries  afterwards  geometry  re- 
mained a  favorite  study,  but  no  substantive  work  fit  to  be  compared 
with  the  Sphere  and  Cylinder  or  the  Conies  was  ever  produced.  One 
great  invention,  trigonometry,  remains  to  be  completed,  but  trigo- 
nometry with  the  Greeks  remained  always  the  instrument  of  astronomy 
and  was  not  used  in  any  other  branch  of  mathematics,  pure  or  applied. 
The  geometers  who  succeed  to  Apollonius  are  professors  who  signalised 
themselves  by  this  or  that  pretty  little  discovery  or  by  some  com- 
mentary on  the  classical  treatises. 

The  force  of  nature  could  go  no  further  in  the  same  direction  than 
the  ingenious  applications  of  exhaustion  by  Archimedes  and  the  por- 
tentous sentences  in  which  Apollonius  enunciates  a  proposition  in 
conies.  A  briefer  symbolism,  an  analytical  geometry,  an  infinitesimal 
calculus  were  wanted,  but  against  these  there  stood  the  tremendous 
authority  of  the  Platonic  and  Euclidean  tradition,  and  no  discoveries 
were  made  in  physics  or  astronomy  which  rendered  them  imperatively 
necessary.  It  remained  only  for  mathematicians,  as  Cantor  says,  to 
descend  from  the  height  which  they  had  reached  and  "in  the  descent 
to  pause  here  and  there  and  look  around  at  details  which  had  been 
passed  by  in  the  hasty  ascent."  The  elements  of  planimetry  were 
exhausted,  and  the  theory  of  conic  sections.  In  stereometry  some- 
thing still  remained  to  be  done,  and  new  curves,  suggested  by  the 
spiral  of  Archimedes,  could  still  be  investigated.  Finally,  the  arith- 
metical determination  of  geometrical  ratios,  in  the  style  of  the  Meas- 
urement of  the  Circle,  offered  a  considerable  field  of  research,  and  to 
these  subjects  mathematicians  now  devoted  themselves.  —  Gow. 

IN.  the  second  century  B.C.  Hypsicles  developed  the  theory  of 
arithmetical  progression  and  added  two  books  of  elements  to 
Euclid's  thirteen,  but  the  chief  mathematical  work  of  this  cen- 

115 


116  A  SHORT  HISTORY  OF  SCIENCE 

tury  was  due  to  Hipparchus,  a  great  astronomer,  and  Hero,  an 
engineer. 

ORBITAL  MOTION  OF  THE  EARTH.  ARISTARCHUS.  —  Before 
dealing  with  Hipparchus  and  Hero,  however,  we  have  to  consider 
the  highly  interesting  and  significant  astronomical  theories  of 
Aristarchus  of  Samos  (270  B.C.-?),  who  was  the  author  of  a 
treatise  On  the  Dimensions  and  Distances  of  the  Sun  and  Moon. 
He  endeavored  to  determine  these  distances  relatively  by  ascer- 
taining or  estimating  the  angular  distance  between  the  two  bodies 
when  the  moon  is  just  half  illuminated,  that  is,  when  the  lines 
joining  sun,  earth,  and  moon  form  a  right  angle  at  the  moon  —  a 
method  which  may  have  been  due  to  Eudoxus.  The  difficulties  of 
this  determination  are  so  serious,  however,  that  no  high  degree 
of  accuracy  could  be  attained,  the  actual  result  of  Aristarchus 
!-§•  of  a  right  angle  —  against  the  true  fr§  —  corresponding  to  a 
ratio  of  about  1  to  19  of  the  two  distances.  Aristarchus  had  no 
trigonometry,  and  no  other  method  of  attacking  this  problem  seems 
to  have  been  known  to  the  Greeks. 

In  his  Sand  Counting  already  mentioned,  Archimedes  says  of 
Aristarchus, 

He  supposes  that  the  fixed  stars  and  the  sun  are  immovable,  but 
that  the  earth  is  carried  round  the  sun  in  a  circle  which  is  in  the  middle 
of  the  course ;  but  the  sphere  of  the  fixed  stars,  lying  with  the  sun  round 
the  same  centre,  is  of  such  a  size  that  the  circle,  in  which  he  supposes 
the  earth  to  move,  has  the  same  ratio  to  the  distance  of  the  fixed  stars 
as  the  centre  of  the  sphere  has  to  the  surface.  But  this  is  evidently 
impossible,  for  as  the  centre  of  the  sphere  has  no  magnitude,  it  follows 
that  it  has  no  ratio  to  the  surface.  It  is  therefore  to  be  supposed  that 
Aristarchus  meant  that  as  we  consider  the  earth  as  the  centre  of  the 
world,  then  the  earth  has  the  same  ratio  to  that  which  we  call  the  world, 
as  the  sphere  in  which  is  the  circle,  described  by  the  earth  according 
to  him,  has  to  the  sphere  of  the  fixed  stars. 

Aristarchus  thus  meets  the  objection  that  motion  of  the  earth 
would  cause  changes  in  the  apparent  positions  of  the  stars  by  as- 
suming that  their  distances  are  so  great  as  to  render  the  motion  of 


DECLINE  OF  ALEXANDRIAN  SCIENCE  117 

the  earth  a  negligible  factor.  Another  reference  to  Aristarchus, 
in  Plutarch,  mentions  an  opinion  that  he 

ought  to  be  accused  of  impiety  for  moving  the  hearth  of  the  world, 
as  the  man  in  order  to  save  the  phenomena  supposed  that  the  heavens 
stand  still  and  the  earth  moves  in  an  oblique  circle  at  the  same  time  as 
it  turns  round  its  axis. 

How  far  this  remarkable  anticipation  of  the  Copernican  theory 
was  a  conviction  rather  than  a  mere  fortunate  speculation  cannot  be 
known,  but  at  any  rate  it  failed  of  that  acceptance  necessary  to  its 
permanence.  In  the  next  century  the  rotation  of  the  earth  on 
its  axis  was  indeed  taught  by  Seleucus,  an  Asiatic  astronomer,  but 
it  was  1700  years  before  these  daring  theories  were  again  advanced. 
Seleucus  also  observed  the  tides,  saying  "that  the  revolution  of 
the  moon  is  opposed  to  the  earth's  rotation,  but  the  air  between  the 
two  bodies  being  drawn  forward  falls  upon  the  Atlantic  Ocean,  and 
the  sea  is  disturbed  in  proportion." 

PLANETAKY  IRREGULARITIES.  —  The  earlier  theory  of  homocen- 
tric  spheres,  while  accounting  more  or  less  successfully  for  the  ap- 
parent motions  of  the  heavenly  bodies,  had  maintained  each  of 
them  at  a  constant  distance  from  the  earth,  and  thus  quite  failed 
to  explain  the  differences  of  brightness  which  were  soon  discovered, 
as  well  as  the  variations  in  the  apparent  size  of  the  moon.  The 
conception  of  motion  in  neither  a  straight  line  nor  a  circle  was  re- 
pugnant to  the  Greek  philosophers,  and  the  difficulty  was  therefore 
met,  first  by  supposing  the  earth  not  to  be  exactly  at  the  centre  of 
the  circular  orbits  about  it,  second  by  introducing  subsidiary 
circles  or  epicycles. 

EXCENTRIC  CIRCULAR  ORBITS.  —  The  complete  planetary  system 
according  to  the  excentric  circle  theory  was  therefore  as  follows.  In 
the  centre  of  the  universe  the  earth,  round  which  moved  the  moon 
in  27  days,  and  the  sun  in  a  year,  probably  in  concentric  circles. 
Mercury  and  Venus  moved  on  circles,  the  centres  of  which  were  al- 
ways on  the  straight  line  from  the  earth  to  the  sun,  so  that  the  earth 
was  always  outside  these  circles,  for  which  reason  the  two  planets 
are  always  within  a  certain  limited  angular  distance  of  the  sun,  from 


118  A  SHORT  HISTORY  OF  SCIENCE 

which  the  ratio  of  the  radius  of  the  excentric  to  the  distance  of  its 
centre  from  the  earth  could  easily  be  determined  for  either  planet. 
Similarly,  the  three  outer  planets  moved  on  excentric  circles,  the 
centres  of  which  lay  somewhere  on  the  line  from  the  earth  to  the  sun, 
but  these  circles  were  so  large  as  always  to  surround  both  the  sun  and 
the  earth.  —  Dreyer. 

It  seems  probable  that  Aristarchus  was  led  through  this  theory 
to  conceive  of  heliocentric  orbits,  and  then  to  reflect  that  the  earth, 
too,  might  revolve  about  the  sun  as  easily  as  the  sun  and  planets 
round  the  earth. 

EPICYCLES.  —  Progress  in  observational  astronomy  increased 
the  number  and  magnitude  of  planetary  irregularities  beyond  the 
stationary  points,  retrograde  motions,  and  variations,  known  to 
Aristarchus,  and  apparently  far  beyond  possible  explanation  by 
the  simple  theory  of  excentric  circles.  The  system  was  therefore 
superseded  by,  or  combined  with,  that  of  epicycles,  not  necessarily 
as  physically  realized,  but  as  at  least  a  geometrical  working  hy- 
pothesis, which  should  conform  to  and  explain  the  observed  phe- 
nomena. 

The  system  of  epicycles  consists  in  superimposing  one  circular 
motion  upon  another,  and  repeating  the  process  to  any  needful 
extent.  The  motion  of  the  moon  about  the  earth,  for  example,  is 
explained  by  assuming  first  a  circle  (later  called  the  deferent)  on 
which  moves  the  centre  of  a  second  smaller  circle  called  the  epi- 
cycle, on  which  the  moon  itself  travels.  By  varying  the  dimensions 
of  both  circles  and  the  velocities  of  the  two  motions,  the  observed 

changes,  both  of  position  and  bright- 
ness of  the  moon,  may  be  more  or  less 
satisfactorily  accounted  for  and  even 
computed  in  advance.  In  particular, 
the  apparent  retrograde  motions  of 
the  planets  in  certain  parts  of  their 
orbits  may  be  explained. 

In  the  figure  E  denotes  the  earth, 
the  large  circle  is  the  deferent  of  a 
planet,  C  the  centre  of  the  epicycle,  PI,  P2,  Pz,  P*  different  pos- 


DECLINE  OF  ALEXANDRIAN  SCIENCE  119 

sible  positions  of  the  planet  in  its  epicycle.  The  distance  of  P 
from  E  obviously  varies;  the  apparent  motion  of  P  being  com- 
pounded of  a  forward  motion  of  C  and  a  backward  motion  at  PI 
is  slower,  at  PS  faster,  than  the  average.  By  suitable  adjust- 
ment of  the  dimensions  and  velocities  there  may  be  retrogression 
for  a  certain  length  of  arc  near  PI,  bounded  by  stationary  points 
where  the  two  motions  seem  to  an  observer  at  E  to  neutralize  each 
other. 

How  far  this  complicated  scheme  really  departed  from  the 
original  postulate  of  uniform  circular  motion  is  sufficiently  in- 
dicated by  Proclus'  remark,  "The  astronomers  who  have  pre- 
supposed uniformity  of  motions  of  the  celestial  bodies  were  ig- 
norant that  the  essence  of  these  movements  is,  on  the  contrary, 
irregularity."  While  in  point  of  fact  the  theory  of  epicycles  and 
that  of  excentric  circles  have  much  in  common,  the  former  gradu- 
ally displaced  the  latter  on  account  of  its  greater  simplicity.  Had 
Aristarchus  worked  out  the  earlier  system  in  full  detail,  the  history 
of  astronomy  might  have  been  considerably  modified. 

At  the  Museum  of  Alexandria  a  school  of  observers  of  whom 
Aristillus  and  Timocharis  were  notable  members  instituted  sys- 
tematic astronomical  observations  with  graduated  instruments 
and  made  a  small  star  catalogue.  Thus  was  laid  a  foundation 
for  the  brilliant  discoveries  of  Hipparchus  and  Ptolemy,  while 
astronomy,  which  had  in  the  work  of  Eudoxus  assumed  the 
character  of  true  science,  though  with  a  too  slender  observational 
basis,  now  became  an  exact  science,  gradually  shedding  its  encum- 
brances of  speculation  and  vague  generalization. 

HIPPARCHUS.  STAR  CATALOGUE.  —  The  next  great  astronomer 
and  much  the  greatest  of  antiquity  is  Hipparchus,  probably  a 
native  of  Bithynia,  but  long  resident  at  Rhodes,  a  city  which 
rivalled  Alexandria  itself  in  its  intellectual  activity.  All  his  works 
but  one  are  lost,  but  his  great  successor  and  disciple,  Ptolemy,  has 
based  his  famous  Almagest  on  the  work  of  Hipparchus  and  it  is 
possible  to  determine  in  a  general  way  how  much  is  to  be  credited 
to  each.  Having  at  his  disposal  the  primitive  star  catalogue  of 
Aristillus  and  Timocharis,  Hipparchus  was  prof  oundly  impressed — 


120  A  SHORT  HISTORY  OF  SCIENCE 

as  was  Tycho  Brahe  centuries  later  —  by  the  sudden  appearance 
in  134  B.C.  in  the  supposedly  changeless  starry  firmament  of  a  new 
star  of  the  first  magnitude.  He  accordingly  set  himself  the  heavy 
task  of  making  a  new  catalogue,  which  ultimately  included  more 
than  1000  stars,  for  the  part  of  the  sky  visible  to  him,  and  "re- 
mained, with  slight  alterations,  the  standard  for  nearly  sixteen 
centuries."  His  list  of  constellations  is  the  basis  of  our  own. 

PRECESSION  OF  THE  EQUINOXES.  —  While  this  great  piece  of 
routine  work  was  deliberately  planned  by  Hipparchus,  not  so  much 
as  an  end  in  itself  as  a  necessary  basis  for  future  investigators,  it 
nevertheless  led  to  his  most  remarkable  discovery,  that  of  the  pre- 
cession of  the  equinoxes.  In  comparing,  namely,  the  positions  of 
certain  stars  with  those  observed  about  150  years  earlier,  he  de- 
tected a  change  of  distance  from  the  equinoctial  point  —  where  the 
celestial  equator  and  the  ecliptic  meet  —  amounting  in  one  case 
to  about  2°.  By  an  inspiration  of  genius,  he  interpreted  this 
correctly  as  due  to  a  slight  progressive  shifting  of  the  equinoctial 
points,  corresponding  to  a  slow  rotation  of  the  earth's  axis,  by 
means  of  which  the  celestial  pole  in  many  thousand  years  describes 
a  complete  circle.  His  estimate  of  36"  per  year  was  considerably 
below  the  actual  value,  which  is  about  50". 

OTHER  ASTRONOMICAL  DISCOVERIES.  PLANETARY  THEORY.  — 
Striving  always  for  greater  accuracy  and  completeness  of  data,  he 
determined  the  length  of  the  year  within  about  six  minutes.  In 
attempting  to  explain  the  annual  motion  of  the  sun,  he  was  aware 
that  the  change  of  direction  is  not  uniform,  and  its  distance  from 
the  earth,  as  shown  by  its  apparent  size,  not  constant.  He  de- 
termined the  length  of  spring  as  94  days,  that  of  summer  as  92^, 
and  by  a  somewhat  complicated  calculation  arrived  at  the  value  -£$ 
as  the  eccentricity  of  the  earth's  position  in  the  sun's  orbit.  These 
determinations  were  naturally  very  difficult  and  imperfect  on  ac- 
count of  the  entire  lack  of  accurate  time  measurement.  Following 
Apollonius,  Hipparchus  devised  a  combination  of  uniform  circular 
motions  which  should  account  for  the  observed  facts  within  the 
limits  of  probable  error  of  observation,  and  in  this  undertaking  he 
was  successful,  the  degree  of  accuracy  of  his  theory  corresponding 
to  that  of  which  his  instruments  were  capable. 


DECLINE  OF  ALEXANDRIAN  SCIENCE 


121 


With  the  more  complicated  lunar  theory  he  was  naturally  less 
successful.  He  is  believed,  however,  to  have  discovered  the  more 
important  irregularities  of  the  moon's  motion,  supposing  it  to 
have  a  circular  orbit  in  a  plane  making  an  angle  of  5°  with  that  of 
the  sun's  orbit  —  the  ecliptic.  The  earth  is  not  at  the  centre, 
but  the  latter  revolves  about  the  earth  in  a  period  of  nine  years. 

Extending  his  study  of  eclipses  to  the  ancient  records  of  the  Chal- 
deans, he  made  substantial  improvements  in  the  theory  of  both 
solar  and  lunar  eclipses,  and  obtained  a  close  approximation  for 
the  distance  of  the  moon.  He  estimated  the  sun's  radius  at  about 
twelve  times  that  of  the  earth,  its  distance  from  the  earth  at  about 
2550  earth-radii,  the  moon's  radius  ^nnr  that  of  the  earth,  its 
distance  about  60  earth-radii.  The  comparison  of  these  figures 
with  Ptolemy's  and  with  the  actual  are  (in  earth-radii)  — 


SUN'S  RADIUS 

SUN'S  DISTANCE 

MOON'S 
RADIUS 

MOON'S 
DISTANCE 

Hipparchus    .     .     . 

12 

2550 

.29 

60 

Ptolemy     .... 

5.5 

1210 

.29 

59 

Actual       .... 

109. 

23,000 

.273 

60£ 

Hipparchus  realized  that  he  had  no  adequate  method  for  de- 
termining these  numbers  for  the  sun. 

The  generally  accepted  order  of  the  planets  had  now  become 
Moon,  Mercury,  Venus,  Sun,  Mars,  Jupiter,  Saturn,  —  an  order 
adopted  very  early  in  Babylonia,  and  received  as  a  more  or  less 
probable  hypothesis  from  this  time  until  that  of  Copernicus.  In 
attempting  to  deal  with  the  motions  of  the  other  planets  as  he  had 
done  with  that  of  the  sun  and  moon,  Hipparchus  was  soon  baffled 
by  lack  of  adequate  data,  and  set  himself  steadfastly  to  supply 
the  need,  resigning  to  more  fortunate  future  astronomers  the  task 
of  interpretation. 

Eudoxus,  more  than  two  centuries  earlier,  had  developed  a  logical 
mathematical  theory  of  the  planetary  motions.  The  more  exact 
methods  and  data  of  Hipparchus  brought  out  the  entire  inadequacy 
of  existing  theory  to  furnish  anything  better  than  a  crude  approxi- 


122  A  SHORT  HISTORY  OF  SCIENCE 

mation  to  the  motions  of  the  planets,  and  showed  the  necessity 
both  of  a  better  theory  and  of  more  complete  observational  data. 
It  is  interesting  to  speculate  on  the  consequences  which  might  have 
resulted  for  astronomical  science  had  the  genius  of  Hipparchus 
adopted  the  daring  heliocentric  theories  of  Aristarchus  instead  of 
adhering  to  the  traditional  geocentric  ideas. 

INVENTION  OF  TRIGONOMETRY. — Not  least  important  among  the 
services  of  Hipparchus  to  science  was  his  laying  the  foundations 
of  trigonometry,  by  constructing  for  astronomical  use  a  table  of 
chords,  equivalent  to  our  tables  of  natural  sines.  He  gave  also  a 
method  for  solving  spherical  triangles.  It  is  said  that  he  first 
indicated  position  on  the  earth  by  latitude  and  longitude  —  the 
germ  of  coordinate  geometry  —  Eratosthenes  having  merely  given 
the  latitude  by  means  of  the  height  of  the  pole-star.  For  mapping 
the  sky  he  used  stereographic  projection,  for  mapping  the  earth 
orthographic. 

To  sum  up  the  chief  work  of  Hipparchus :  —  he  made  very  effec- 
tive use  of  extant  records  of  earlier  astronomers  with  critical  con- 
sideration of  their  value;  he  made  a  prolonged  and  systematic 
series  of  observations  with  the  best  available  instruments;  he 
worked  out  a  consistent  mathematical  theory  of  the  motions  of  the 
heavenly  bodies  so  far  as  his  data  warranted;  he  made  a  new 
catalogue  of  1080  stars,  with  the  classification  by  magnitude  still  in 
use;  he  discovered  the  precession  of  the  equinoxes;  he  laid  the 
foundations  of  trigonometry. 

Delambre,  the  great  French  historian  of  astronomy,  says :  — 

When  we  consider  all  that  Hipparchus  invented  or  perfected  and 
reflect  upon  the  number  of  his  works  and  the  mass  of  calculations 
which  they  imply,  we  must  regard  him  as  one  of  the  most  astonishing 
men  of  antiquity,  and  as  the  greatest  of  all  in  the  sciences  which  are  not 
purely  speculative,  and  which  require  a  combination  of  geometrical 
knowledge  with  a  knowledge  of  phenomena,  to  be  observed  only  by 
diligent  attention  and  refined  instruments. 

In  spite  of  these  brilliant  achievements,  the  position  of  Apollonius 
and  Hipparchus  had  become  relatively  isolated  under  the  prevalent 


DECLINE   OF  ALEXANDRIAN   SCIENCE  123 

Stoic  philosophy,  which  was  attended  with  a  reversion  to  primitive 
cosmical  notions.  Even  in  Hipparchus  a  somewhat  critical  atti- 
tude, excellent  in  its  immediate  results,  has  been  regarded  by  some 
as  foreshadowing  the  period  of  decadence  which  actually  followed. 
Astronomy  is  to  remain  nearly  stationary  for  sixteen  centuries. 

INVENTIONS.  CTESIBUS  AND  HERO.  —  In  the  period  of  civil 
war  following  the  death  of  Alexander  and  followed  in  turn  by 
Roman  conquest,  much  attention  was  naturally  devoted  to  the 
invention  and  improvements  of  military  engines.  Compressed 
air  came  into  use  as  a  motive  power  and  the  foundations  of 
pneumatics  were  laid. 

Ctesibus,  a  barber  of  Alexandria,  distinguished  by  his  mechanical 
inventions,  and  his  follower  Hero  (or  Heron)  who  flourished  in  the 
latter  part  of  the  second  century  B.C.,  made  notable  inventions 
and  some  real  contributions  to  mathematical  science.  The  works 
attributed  to  Hero,  on  the  basis  of  a  great  quantity  of  confused 
and  doubtful  material,  include :  —  a  Mechanics,  treating  of  centres 
of  gravity  and  of  the  lever,  wedge,  screw,  pulley,  and  wheel  and 
axle;  various  works  on  military  engines  and  mechanical  toys,  a 
Pneumatics  —  the  oldest  work  extant  on  the  properties  of  air 
and  vapor  —  describing  many  machines,  among  others  a  fire-en- 
gine, a  water-clock,  organs,  and  in  particular  a  steam-engine  which 
we  may  regard  as  a  remote  precursor  of  our  modern  steam  turbine. 
Many  of  the  machines  depend  for  their  action  on  the  flow  of  water 
into  a  vacuum,  which  Hero,  having  no  conception  of  atmospheric 
pressure,  attributed  to  nature's  "abhorrence"  of  a  vacuum. 
He  arrived  at  the  important  law  for  the  lever  and  the  pulley: 
"The  ratio  of  the  times  is  equal  to  the  inverse  ratio  of  the  forces 
applied."  The  Dioptra,  a  treatise  on  a  kind  of  rudimentary  theod- 
olite,  discusses  such  engineering  problems  as  finding  differences 
of  level,  cutting  a  tunnel  through  a  hill,  sinking  a  vertical  shaft  to 
meet  a  horizontal  tunnel,  measuring  a  field  without  entering  it,  etc. 
The  instrument  employed  is  described  as  a  straight  plank,  8  or  9 
feet  long,  mounted  on  a  stand  but  capable  of  turning  through  a 
semicircle.  It  was  adjusted  by  screws,  turning  cog-wheels. 
There  was  an  eye-piece  at  each  end  and  a  water  level  at  the  side. 


124 


A  SHORT  HISTORY  OF  SCIENCE 


With  it  two  poles,  bearing  disks,  were  used,  exactly  as  by  modern 
surveyors.  A  cyclometer  for  a  carriage  is  also  described,  with  a 
series  of  cog-wheels  and  an  index. 

In  optics  he  shows  that  under  the  law  of  equal  angles  of  incidence 
and  reflection,  the  path  described  by  the  ray  is  a  minimum. 

HERO'S  TRIANGLE  FORMULA.  —  His  Geodesy,  —  also  the  Dioptra 
—  contains  the  well-known  formula  for  the  area  of  a  triangle 


j 
V 


a  +  b  +  c       a  +  b  —  c       b  +  c  —  a      c 
~  2  2 


a  —  b 


which,  since  it  involves  the  multiplication  of  four  lengths  together, 
is  heterodox  from  the  Euclidean  standpoint. 

ABC  is  the  given  triangle  of  sides  a,  6,  c,  touching  its  inscribed  circle 
at  D,  E,  and  F.     Taking  BJ  =  AD,  we  have  CJ  =  J(a  +  b  +  c)  and 

area  ABC  =  twice  area  CJM  . 

Draw  perpendiculars  to  CM 
at  M  and  to  CJ  at  B,  meet- 
ing in  H.  A  semicircle  on  the 
diameter  CH  will  pass  through 
both  M  and  B.  The  sum 
of  the  angles  CHB  and  CMB 
is  180°;  the  triangles  BCH 
and  MAD  are  therefore  simi- 
lar, 

so  that  BC:BH  =  AD:  MD,  or  BC:BJ  =  BH:  ME. 
Also  the  triangles  BGH  and  EGM  are  similar, 

so  that  BH:ME  =  BG:EG  and  BC:BJ  =  BG:EG, 
whence   BC  +  B  J  :  BJ  =  BG  +EG  :  EG,  that  is, 

CJ:BJ  =  BE:EGsind~CJ2:BJ  X  CJ  =  CE  XBE:CE  X  EG, 

that   is,   CJ2  :  BJ  X  C  J  =  BE  X  CE  :  EM2,  which  is  equivalent   to 

BE  XCE:CJ  XEM  =  CJ  X  EM  :  BJ  X  CJ. 

But    CJ  X  EM  =  £,     CE  =  J(a  +  b  -  c),  etc., 
whence    4  K*  =  (a  +  b  +  c)  (a  +  b  -  c)  (6  +  c  -  a)  (c  +  a  -  6). 


DECLINE  OF  ALEXANDRIAN  SCIENCE  125 

A  triangle  with  sides  13,  14,  15  is  selected  as  an  illustration.    Its 
area  is 

V21  X  6  X  7  X  8  =  84. 

This  work  seems  to  have  become  a  standard  authority  for 
generations  of  surveyors,  and  thus  in  course  of  time  to  have  lost 
much  of  its  identity  by  successive  changes.  The  whole  spirit  of 
the  work  is  rather  Egyptian  than  Greek,  that  of  the  practical 
engineer  as  distinguished  from  that  of  the  mathematician,  thus  in 
a  measure  a  reversion  to  the  aims  of  the  Ahmes  manuscript.  "  Let 
there  be  a  circle  with  circumference  22,  diameter  7.  To  find  its  area. 
Do  as  follows.  7  X  22  =  154  and  ^  =  38J.  That  is  the  area." 

Some  of  Hero's  methods  indicate  knowledge  of  the  new  trigo- 
nometry of  Hipparchus  and  of  the  principle  of  coordinates.  Thus 
he  finds  areas  of  irregular  boundary  by  counting  inscribed  rec- 
tangles, a  process  corresponding  to  the  use  of  coordinate  paper. 

From  Hero  date  such  time-honored  problems  as  that  of  the 
pipes.  A  vessel  is  filled  by  one  pipe  in  time  t\,  by  another  in 
time  t?.  How  long  will  it  take  to  fill  it  when  both  pipes  are  used  ? 

He  defines  spherical  triangles  and  proves  simple  theorems  about 
them :  —  for  example,  that  the  angle-sum  lies  between  180°  and 
540°.  He  determines  the  volume  of  irregular  solids  by  measuring 
the  water  they  displace.  Having  by  a  blunder  introduced  V—  63 
he  confuses  it  with  V63. 

INDUCTIVE  ARITHMETIC.  NICOMACHUS.  —  As  in  the  case  of 
astronomy,  progress  in  geometry  now  lags  and  finally  ceases  alto- 
gether. About  100  A. D.  a  final  era  of  Greek  mathematical  science, 
predominantly  arithmetical  in  character,  begins  with  Nicomachus 
of  Judea,  whose  work  remained  the  basis  of  European  arithmetic 
until  the  introduction  of  the  Arabic  arithmetic  a  thousand  years 
later.  He  enunciates  curious  theorems  about  squares  and  cubes, 
for  example  :  —  In  the  series  of  odd  numbers  from  1,  the  first  term 
is  the  first  cube,  the  sum  of  the  next  two  is  the  second,  of  the 
next  three  the  third,  etc.,  —  doubtless  simple  observation  and 
induction.  He  refers  to  proportion  as  very  necessary  to  "  natural 
science,  music,  spherical  trigonometry  and  planimetry,"  and 
discusses  various  cases  in  great  detail. 


126  A  SHORT  HISTORY  OF  SCIENCE 

Mathematics  had  passed  from  the  study  of  the  philosopher  to 
the  lecture-room  of  the  undergraduate.  We  have  no  more  the  grave 
and  orderly  proposition,  with  its  deductive  proof.  Nicomachus 
writes  a  continuous  narrative,  with  some  attempt  at  rhetoric,  with 
many  interspersed  allusions  to  philosophy  and  history.  But  more  im- 
portant than  any  other  change  is  this,  that  the  arithmetic  of  Nico- 
machus is  inductive,  not  deductive.  It  retains  from  the  old  geometrical 
style  only  its  nomenclature.  Its  sole  business  is  classification,  and 
all  its  classes  are  derived  from,  and  are  exhibited  in,  actual  numbers. 
But  since  arithmetical  inductions  are  necessarily  incomplete,  a  general 
proposition,  though  prima  facie  true,  cannot  be  strictly  proved  save 
by  means  of  an  universal  symbolism.  Now  though  geometry  was 
competent  to  provide  this  to  a  certain  extent,  yet  it  was  useless  for 
precisely  those  propositions  in  which  Nicomachus  takes  most  interest. 
The  Euclidean  symbolism  would  not  show,  for  instance,  that  all  the 
powers  of  5  end  in  5  or  that  the  square  numbers  are  the  sums  of  the 
series  of  odd  numbers.  What  was  wanted,  was  a  symbolism  similar 
to  the  ordinary  numerical  kind,  and  thus  inductive  arithmetic  led 
the  way  to  algebra.  —  Gow. 

PTOLEMY  AND  THE  PTOLEMAIC  SYSTEM.  —  With  Claudius 
Ptolemy,  in  the  second  century  of  our  era,  Greek  astronomy 
reaches  its  definitive  formulation.  In  the  260  years  which  had 
elapsed  since  Hipparchus  no  progress  of  consequence  had  been 
made. 

Of  Hipparchus,  from  whom  he  inherited  so  much,  Ptolemy 
writes :  — 

It  was,  I  believe,  for  these  reasons  and  especially  because  he  had 
not  received  from  his  predecessors  as  many  accurate  observations  as 
he  has  left  to  us,  that  Hipparchus,  who  loved  truth  above  everything, 
only  investigated  the  hypotheses  of  the  sun  and  moon,  proving  that 
it  was  possible  to  account  perfectly  for  their  revolutions  by  combi- 
nations of  circular  and  uniform  motions,  while  for  the  five  planets, 
at  least  in  the  writings  which  he  has  left,  he  has  not  even  com- 
menced the  theory,  and  has  contented  himself  with  collecting  sys- 
tematically the  observations,  and  showing  that  they  did  not  agree 
with  the  hypotheses  of  the  mathematicians  of  his  time.  He  explained 
in  fact  not  only  that  each  planet  has  two  kinds  of  inequalities  but  also 


* 


DECLINE  OF  ALEXANDRIAN   SCIENCE  127 

that  the  retrogradations  of  each  are  variable  in  extent,  while  the  other 
mathematicians  had  only  demonstrated  geometrically  a  single  in- 
equality and  a  single  arc  of  retrograde  motion ;  and  he  believed  that 
these  phenomena  could  not  be  represented  by  excentric  circles  nor  by 
epicycles  carried  on  concentric  circles,  but  that,  it  would  be  necessary 
to  combine  the  two  hypotheses.  —  Dreyer. 

The  instruments  used  by  Ptolemy  for  his  astronomical  observa- 
tions included:  —  the  "Ptolemaic  rule,"  consisting  of  a  rod  with 
sights  pivoted  to  a  vertical  rod,  the  angle  at  the  junction  being 
measured  by  the  subtended  chord ;  the  armillary  circle,  a  copper 
or  bronze  ring  marked  in  degrees  and  mounted  in  the  meridian 
plane  on  a  post.  A  second  movable  ring  is  fitted  into  this  with 
pegs  diametrically  opposite  each  other,  by  means  of  which  the  sun's 
midday  height  could  be  measured ;  the  armillary  sphere,  similar  in 
principle  but  somewhat  more  complicated ;  the  astrolabe  or  as- 
tronomical ring  for  measuring  either  horizontal  or  vertical  angles. 
Like  the  Chaldeans  Ptolemy  also  used  meridian  quadrants  of 
masonry.  Time  was  still  measured  by  the  flow  of  water,  with 
apparatus  considerably  improved  by  Ctesibus  and  Hero.  The 
numerous  observations  of  Ptolemy  were  made  during  the  period 
125-151  A.D.  and  he  was  in  Alexandria  in  139. 

One  of  his  observations  he  describes  as  follows : 

In  the  2d  year  of  Antoninus,  the  9th  day  of  Pharmonthe,  the 
sun  being  near  setting,  the  last  division  of  Taurus  being  on  the 
meridian  (that  is,  5^  equinoctial  hours  after  noon),  the  moon  was  in 
3  degrees  of  Pisces,  by  her  distance  from  the  sun  (which  was  92  de- 
grees, 8  minutes) ;  and  hah0  an  hour  after,  the  sun  being  set,  and 
the  quarter  of  Gemini  on  the  meridian,  Regulus  appeared,  by  the 
other  circle  of  the  astrolabe,  57^  degrees  more  forwards  than  the  moon 
in  longitude.  —  Whewell. 

THE  ALMAGEST.  —  In  his  celebrated  Syntaxis,  better  known 
from  Arabic  translations  as  the  Almagest,  Ptolemy  undertakes  to 
present  for  the  first  time  the  whole  astronomical  science  of  his  age. 

In  Book  I  he  reviews  the  fundamental  astronomical  data  thus :  — 


128  A  SHORT  HISTORY  OF  SCIENCE 

The  earth  is  a  sphere,  situated  in  the  centre  of  the  heavens;  if 
it  were  not,  one  side  of  the  heavens  would  appear  nearer  to  us  than 
the  other,  and  the  stars  would  be  larger  there ;  if  it  were  on  the  celes- 
tial axis  but  nearer  to  one  pole,  the  horizon  would  not  bisect  the  equator 
but  one  of  its  parallel  circles;  if  the  earth  were  outside  the  axis, 
the  ecliptic  would  be  divided  unequally  by  the  horizon.  The  earth 
is  but  as  a  point  in  comparison  to  the  heavens,  because  the  stars  appear 
of  the  same  magnitude  and  at  the  same  distances  inter  se,  no  matter 
where  the  observer  goes  on  the  earth.  It  has  no  motion  of  translation, 
first,  because  there  must  be  some  fixed  point  to  which  the  motions  of  the 
others  may  be  referred,  secondly,  because  heavy  bodies  descend  to  the 
centre  of  the  heavens  which  is  the  centre  of  the  earth.  And  if  there  was 
a  motion,  it  would  be  proportionate  to  the  great  mass  of  the  earth  and 
would  leave  behind  animals  and  objects  thrown  into  the  air.  This 
also  disproves  the  suggestion  made  by  some,  that  the  earth,  while 
immovable  in  space,  turns  round  its  own  axis,  which  Ptolemy  ac- 
knowledges would  simplify  matters  very  much.1 

Chapter  IX  explains  the  calculation  of  a  table  of  chords.  Start- 
ing with  the  chords  of  60°  and  72°,  already  known  as  sides  of  regular 
polygons,  he  devises  ingenious  geometrical  methods  for  finding 
chords  of  differences  and  of  half-angles.  Thus  he  computes  the 
chords  for  12°,  6°,  3°,  If  °,  and  f  °.  Hipparchus  had  already  com- 
puted such  a  table,  but  Ptolemy  completes  it  by  showing  that 

f  chord  1J°  <  chord  1°  <  -J  chord  f  ° 

and  thence  deriving  close  approximations  for  the  chords  of  1° 
and  |°  and  constructing  a  table  for  each  half -degree  up  to  180°. 
His  results  are  expressed  in  sexagesimal  fractions  of  the  radius  (of 
which  they  are  thus  numerically  independent)  and  are  equivalent 
in  accuracy  to  five  decimals  in  our  notation.  He  also  employs 
our  present  method  of  interpolation,  skilfully.  This  chapter  is 
the  culmination  of  Greek  trigonometry,  which  owed  its  further 
development  to  Indian  and  Arabic  mathematicians. 

1  "For  Ptolemy  more  geometer  and  astronomer  than  philosopher,  the  astronomer 
who  seeks  hypotheses  adapted  to  save  the  apparent  movements  of  the  stars  knows 
no  other  guide  than  the  rule  of  greatest  simplicity :  It  is  necessary  as  far  as  possible 
to  apply  the  simplest  hypotheses  to  the  celestial  movements,  but  if  they  do  not 
suffice,  it  is  necessary  to  take  others  which  fit  better. "  —  Duhem. 


DECLINE  OF  ALEXANDRIAN  SCIENCE  129 

In  Books  III,  IV,  and  V,  Ptolemy  discusses  the  apparent  motions 
and  distances  of  the  sun  and  moon  by  means  of  excentrics  and 
epicycles,  his  method  for  determining  the  moon's  distance  being 
substantially  the  same  as  the  modern.  Book  V  describes  the  con- 
struction and  use  of  his  chief  instrument,  the  astrolabe.  Book  VI" 
deals  with  eclipses,  using  a  value  of  TT  equivalent  to  our  3.1416. 
He  determines  the  distance  of  the  sun,  following  Hipparchus,  by 
observing  the  breadth  of  the  earth's  shadow  when  the  moon 
crosses  it  at  an  eclipse.  Books  VII  and  VIII  contain  a  catalogue 
of  1028  stars  based  on  that  of  Hipparchus,  and  a  discussion  of 
precession  of  the  equinoxes,  with  a  close  determination  of  the 
unequal  intervals  between  successive  vernal  and  autumnal  equi- 
noxes. The  remainder  of  the  treatise  is  devoted  to  the  planets, 
containing  Ptolemy's  chief  original  contributions. 

While  Ptolemy  did  not  take  advantage  of  the  better  data  at 
his  command  to  improve  the  theory  of  the  sun's  motion,  he  did 
make  substantial  progress  with  that  of  the  moon,  the  discrepancies 
for  which  rarely  exceed  10',  which  represented  about  the  maximum 
precision  of  his  instruments.  Hipparchus  had  assumed  the  moon 
to  have  a  motion  representable  by  one  circle  with  the  earth  as  a 
centre  and  by  an  epicycle  with  its  centre  upon  this.  Discrepancies 
between  observed  and  computed  positions  led  Ptolemy,  bound  asv 
he  was  by  the  Aristotelian  dictum  that  celestial  bodies  can  move 
only  in  circular  paths,  to  modify  this  by  making  the  first  circle 
excentric  to  the  earth,  the  line  joining  the  centres  of  the  circle 
and  the  earth  being  itself  assumed  to  revolve.  This  theory,  while 
giving  results  of  sufficient  accuracy  for  the  observations  at  certain 
positions  of  the  moon,  exaggerated  considerably  the  variation  of 
its  distance  from  the  earth,  making  this  at  times  almost  twice 
as  great  as  at  others. 

For  the  five  planets,  or  "wandering  stars,"  he  also  assumed  ex- 
centric  deferents,  and  as  a  further  means  of  accounting  for  dis- 
crepancies, an  additional  point,  in  line  with  the  centres  of  earth  and 
deferent,  called  the  "equant,"  with  respect  to  which  the  centre  of 
the  epicycle  would  have  uniform  angular  velocity.  The  planes  of 
the  epicycles  were  slightly  inclined  to  that  of  the  ecliptic. 


130  A  SHORT  HISTORY  OF  SCIENCE 

Thus  in  the  figure,  C  is  the  centre  of  the  circular  deferent,  E  the 
earth  and  E'  the  equant.  The  center  A  of  the  epicycle  travels 
at  such  a  rate  that  the  line  E'A  has  uniform 
angular  velocity.  The  planet  J  travels  in 
an  epicycle  about  A.  These  assumptions 
afforded  the  needful  freedom  for  a  fairly  close 
approximation  to  observed  planetary  motions, 
the  mathematical  computations  involved  be- 
coming naturally  quite  elaborate.  Ptolemy 
disclaimed  the  power  of  determining  the  distances  or  even  the 
order  of  the  planets. 

That  the  system  as  a  whole  deserves  our  admiration  as  a  ready 
means  of  constructing  tables  of  the  movements  of  sun,  moon,  and 
planets,  cannot  be  denied.  Nearly  in  every  detail  (except  the  varia- 
tion of  distance  of  the  moon)  it  represented  geometrically  these  move- 
ments almost  as  closely  as  the  simple  instruments  then  in  use  enabled 
observers  to  follow  them,  and  it  is  a  lasting  monument  to  the  great 
mathematical  minds  by  whom  it  was  gradually  developed. 

To  the  modern  mind,  accustomed  to  the  heliocentric  idea,  it  is 
difficult  to  understand  why  it  did  not  occur  to  a  mathematician  like 
Ptolemy  to  deprive  all  the  outer  planets  of  their  epicycles,  which  were 
nothing  but  reproductions  of  the  earth's  annual  orbit  transferred 
to  each  of  these  planets,  and  also  to  deprive  Mercury  and  Venus  of 
their  deferents,  and  place  the  centres  of  their  epicycles  in  the  sun,  as 
Heraclides  had  done.  .  .  .  The  system  of  Ptolemy  was  a  mere  geo- 
metrical representation  of  celestial  motions,  and  did  not  profess  to 
give  a  correct  picture  of  the  actual  system  of  the  world.  .  .  .  For 
more  than  1400  years  it  remained  the  Alpha  and  Omega  of  theoretical 
astronomy,  and  whatever  views  were  held  as  to  the  constitution  of 
the  world,  Ptolemy's  system  was  almost  universally  accepted  as  the 
foundation  of  astronomical  science.  —  Dreyer. 

After  Ptolemy  we  have  no  record  of  any  important  advance  in 
astronomy  for  nearly  1000  years. 

In  reviewing  Greek  astronomy  Berry  says, 

The  Greeks  inherited  from  their  predecessors  a  number  of  observa- 
tions, many  of  them  executed  with  considerable  accuracy,  which  were 


DECLINE  OF  ALEXANDRIAN  SCIENCE  131 

nearly  sufficient  for  the  requirements  of  practical  life,  but  in  the  matter 
of  astronomical  theory  and  speculation,  in  which  their  best  thinkers 
were  very  much  more  interested  than  in  the  detailed  facts,  they  re- 
ceived virtually  a  blank  sheet  on  which  they  had  to  write  (at  first  with 
indifferent  success)  their  speculative  ideas.  A  considerable  interval 
of  time  was  obviously  necessary  to  bridge  over  the  gulf  separating 
such  data  as  the  eclipse  observations  of  the  Chaldeans  from  such 
ideas  as  the  harmonical  spheres  of  Pythagoras;  and  the  necessary 
theoretical  structure  could  not  be  erected  without  the  use  of  mathemati- 
cal methods  which  had  gradually  to  be  invented.  That  the  Greeks, 
particularly  in  early  times,  paid  little  attention  to  making  observations, 
is  true  enough,  but  it  may  fairly  be  doubted  whether  the  collection 
of  fresh  material  for  observations  would  really  have  carried  astronomy 
much  beyond  the  point  reached  by  the  Chaldean  observers.  When 
once  speculative  ideas,  made  definite  by  the  aid  of  geometry,  had 
been  sufficiently  developed  to  be  capable  of  comparison  with  observa- 
tion, rapid  progress  was  made.  The  Greek  astronomers  of  the  scientific 
period,  such  as  Aristarchus,  Eratosthenes,  and  above  all  Hipparchus, 
appear  moreover  to  have  followed  in  their  researches  the  method  which 
has  always  been  fruitful  in  physical  science  —  namely,  to  frame  pro- 
visional hypotheses,  to  deduce  their  mathematical  consequences,  and 
to  compare  these  with  the  results  of  observation.  There  are  few  better 
illustrations  of  genuine  scientific  caution  than  the  way  in  which  Hip- 
parchus, having  tested  the  planetary  theories  handed  down  to  him 
and  having  discovered  their  insufficiency,  deliberately  abstained  from 
building  up  a  new  theory  on  data  which  he  knew  to  be  insufficient, 
and  patiently  collected  fresh  material,  never  to  be  used  by  himself, 
that  some  future  astronomer  might  thereby  be  able  to  arrive  at  an 
improved  theory. 

Of  positive  additions  to  our  astronomical  knowledge  made  by  the 
Greeks  the  most  striking  in  some  ways  is  the  discovery  of  the  ap- 
proximately spherical  form  of  the  earth,  a  result  which  later  work  has 
only  slightly  modified.  But  their  explanation  of  the  chief  motions 
of  the  solar  system  and  their  resolution  of  them  into  a  comparatively 
small  number  of  simpler  motions  was,  in  reality,  a  far  more  important 
contribution,  though  the  Greek  epicyclic  scheme  has  been  so  re- 
modelled, that  at  first  sight  it  is  difficult  to  recognize  the  relation  be- 
tween it  and  our  modern  views.  The  subsequent  history  will,  however, 
show  how  completely  each  stage  in  the  progress  of  astronomical  science 
has  depended  on  those  that  preceded. 


132  A  SHORT  HISTORY  OF  SCIENCE 

When  we  study  the  great  conflict  in  the  time  of  Copernicus  be- 
tween the  ancient  and  modern  ideas,  our  sympathies  naturally  go  out 
towards  those  who  supported  the  latter,  which  are  now  known  to  be 
more  accurate,  and  we  are  apt  to  forget  that  those  who  then  spoke 
in  the  name  of  the  ancient  astronomy  and  quoted  Ptolemy  were  indeed 
believers  in  the  doctrines  which  they  had  derived  from  the  Greeks, 
but  that  their  methods  of  thought,  their  frequent  refusal  to  face  facts, 
and  their  appeals  to  authority,  were  all  entirely  foreign  to  the  spirit  of 
the  great  men  whose  disciples  they  believed  themselves  to  be. 

OTHER  WORKS  OF  PTOLEMY.  —  In  spite  of  his  scientific  attain- 
ments Ptolemy  did  not  disdain  to  write  an  elaborate  treatise  on 
astrology.  In  a  lost  work  on  geometry,  Ptolemy  made  the  first 
known  of  the  interminable  series  of  attempts  to  give  a  formal 
proof  of  Euclid's  parallel  postulate,  an  attempt  naturally  fore- 
doomed to  failure. 

In  a  great  treatise  on  geography,  hardly  less  important  than  the 
Almagest,  Ptolemy  gave  a  description  of  the  known  earth,  locating 
not  less  than  5000  places  by  latitude  and  longitude.  He  even  gave 
in  addition  to  position  the  maximum  length  of  day  for  39  points 
in  India,  a  land  probably  better  known  at  this  period  than  in  the 
time  of  Mercator,  near  the  end  of  the  sixteenth  century.  Ptolemy 
reckoned  longitude  from  the  "Fortunate  Isles,"  —the  western 
boundary  of  the  known  world.  Various  methods  of  projection 
were  discussed  in  connection  with  directions  for  map  drawing. 

Ptolemy  also  wrote  on  sound  and  on  optics,  dealing  particularly 
in  the  latter  with  refraction,  with  what  has  been  called  "  the  oldest 
extant  example  of  a  collection  of  experimental  measures  in  any 
other  subject  than  astronomy."  He  discovered  by  careful  exper- 
iment and  induction  the  law  that  light-rays  passing  from  a  rarer 
to  a  denser  medium  are  bent  towards  the  perpendicular,  and  in- 
vented a  simple  apparatus  for  measuring  angles  of  incidence 
and  reflection. 

PAPPUS.  —  The  last  two  of  the  great  Greek  mathematicians  were 
Pappus  and  Diophantus,  who  lived  in  Alexandria  about  300  A.D. 

The  most  important  work  of  Pappus  is  his  Collections,  in  eight 
books,  of  which  all  but  the  first  and  a  part  of  the  second  are  pre- 


DECLINE  OF  ALEXANDRIAN  SCIENCE  133 

served.  In  this  he  comments  fully  on  the  most  important  Greek 
mathematical  works  known  to  him,  making  his  treatise  of  the 
highest  historical  value,  particularly  in  its  careful  summaries  of 
books  which  have  been  lost.  Book  I  and  most  of  Book  II  are 
missing,  the  third  reviews  the  various  solutions  of  the  duplication 
of  the  cube,  adding  Pappus'  own,  and  discusses  the  regular  in- 
scribed polyhedrons;  the  fourth  deals  with  several  less  simple 
geometrical  matters,  including  the  higher  curves,  spirals,  con- 
choid, quadratrix,  etc.,  the  problem  of  describing  a  circle  tan- 
gent to  three  given  circles  which  touch  each  other;  the  fifth  is 
also  geometrical.  In  Book  VI  Pappus  gives  the  mathematical 
basis  for  the  Ptolemaic  astronomy,  —  i.e.  trigonometry  and 
optics.  Book  VII  contains  his  well-known  theorems,  some- 
times mistakenly  attributed  to  Gulden,  that  the  volume  of  a 
solid  of  revolution  is  equal  to  the  product  of  the  area  of  the  re- 
volving figure  and  the  length  of  the  path  of  its  centre  of  gravity, 
and  that  the  surface  generated  is  equal  to  the  product  of  the  perim- 
eter and  the  length  of  the  circular  path  described  by  its  centre  of 
gravity.  In  this  final  book  he  undertakes  to  deal  with  certain 
mechanical  problems  "more  clearly  and  truly"  than  his  prede- 
cessors have  done.  These  include,  for  example,  centre  of  gravity, 
inclined  planes,  the  moving  of  a  given  weight  by  a  given  power 
with  the  help  of  cog-wheels,  the  determination  of  the  diameter  of 
a  broken  cylinder.  The  whole  is  somewhat  weak  on  the  arith- 
metical side. 

With  the  political  decline  of  Greece  and  the  awakening  to  in- 
tellectual activity  of  great  Semitic  and  Egyptian  populations, 
mathematical  science  changed  radically  from  the  traditional  de- 
ductive geometry,  to  an  arithmetical  and  algebraic  science  in 
harmony  with  the  aptitudes  which  have  characterized  these  races. 
Thus  Nicomachus  as  we  have  seen  was  of  Jewish  antecedents, 
Hero  an  Egyptian  in  his  point  of  view  and  his  scientific  tendencies. 

BEGINNINGS  OF  ALGEBRA.  DIOPHANTUS.  —  Diophantus  was 
active  in  Alexandria  in  the  first  half  of  the  fourth  century  A.D., 
though  we  know  so  little  about  him  that  even  his  precise  name 
is  doubtful.  His  chief  work  is  his  Arithmetic,  which  is  extant 


134  A  SHORT  HISTORY  OF  SCIENCE 

however  only  in  somewhat  mutilated  form.  It  is  the  first 
known  treatise  on  algebra,  and  is  devoted  to  the  solution  of 
equations,  employing  algebraic  symbols  and  analytical  methods. 
Euclid  had  given  the  geometrical  equivalent  of  the  solution  of  a 
quadratic  equation,  and  Hero  could  solve  the  same  problem  alge- 
braically but  lacked  a  satisfactory  symbolism.  The  algebra  of 
Diophantus  was  therefore  not  a  sudden  invention,  but  the  result 
of  gradual  evolution  during  several  centuries  of  increasing  interest 
in  arithmetical  problems,  and  declining  vogue  of  the  abstract 
Euclidean  geometry. 

Writers  on  the  history  of  algebra  distinguish  three  classes  or 
methods  of  algebraic  expression :  — 

(a)  the  rhetorical,  where  no  symbols  are  used,  but  every  term 
and  operation  is  described  in  full.  This  was  the  only  method 
known  before  Diophantus,  and  was  later  in  vogue  in  western 
Europe  until  the  fifteenth  century; 

(6)  the  syncopated,  which  replaces  common  words  and  operations 
by  abbreviations,  but  conforms  to  the  ordinary  rules  of  syntax. 
This  was  the  style  of  Diophantus ; 

(c)  the  symbolical  or  modern,  using  symbols  only,  without  words. 

The  syncopated  method  may  be  illustrated  by  the  following 
passage  from  Heath's  Diophantus :  — 

Let  it  be  proposed  then  to  divide  16  into  two  squares.  And  let 
the  first  be  supposed  to  be  IS ;  therefore  the  second  will  be  16*7  —  IS. 
Thus  16*7  —  IS  must  be  equal  to  a  square.  I  form  the  square  from 
any  number  of  N's  minus  as  many  *7's  as  there  are  in  the  side  of  16  IPs. 
Suppose  this  to  be  2N  -  4*7.  Thus  the  square  itself  will  be  4S  16*7- 
IQN  etc. 

In  his  Arithmetic,  which  is  really  a  treatise  on  algebra,  Diophan- 
tus represents  the  (single)  unknown  by  the  Greek  sigma  —  all  the 
other  letters  of  the  Greek  alphabet  standing  for  definite  numbers 
—  with  successive  powers  to  the  sixth  inclusive.  If  he  requires 
two  unknowns  he  admits  only  one  at  a  time.  His  originality  and 
power  in  the  solution  of  problems  are  amply  shown,  though  the 
solutions  are  rarely  complete.  For  quadratic  equations,  for  ex- 


DECLINE  OF  ALEXANDRIAN  SCIENCE  135 

ample,  he  gives  but  one  root,  even  when  both  are  positive.  Nega- 
tive numbers  are  for  him  unreal,  and  he  also  avoids  the  irrational. 
He  admits  fractional  results  however,  and  is  indeed  the  first  Greek 
for  whom  a  fraction  is  a  number  rather  than  a  mere  ratio  of  two 
numbers.  For  the  solution  of  pure  equations  his  rule  is:  "If  a 
problem  leads  to  an  equation  containing  the  same  powers  of  the 
unknown  on  both  sides  but  not  with  the  same  coefficients,  you 
must  deduct  like  from  like  till  only  two  equal  terms  remain. 
But  when  on  one  side  or  both  some  terms  are  negative,  you  must 
add  the  negative  terms  to  both  sides  till  all  the  terms  are  positive 
and  then  deduct  as  before  stated." 

His  method  for  general  quadratics  is  not  given.  He  solves  one 
cubic  equation,  also  particular  cases  of  the  indeterminate  equation 
Ax2  +  Bx  +  C  =  Y2.  The  modern  so-called  Diophantine  equa- 
tions involving  the  solution  in  integers  of  one  or  more  indeter- 
minate equations,  do  not  occur  in  his  own  extant  work. 

In  130  indeterminate  equations,  which  Diophantus  treats,  there 
are  more  than  50  different  classes.  ...  It  is  therefore  difficult  for  a 
modern,  after  studying  100  Diophantic  equations,  to  solve  the  101st ; 
and  if  we  have  made  the  attempt,  and  after  some  vain  endeavours  read 
Diophantus '  own  solution,  we  shall  be  astonished  to  see  how  suddenly 
he  leaves  the  broad  high-road,  dashes  into  a  side-path  and  with  a  quick 
turn  reaches  the  goal,  often  enough  a  goal  with  reaching  which  we 
should  not  be  content ;  we  expected  to  have  to  climb  a  toilsome  path, 
but  to  be  rewarded  at  the  end  by  an  extensive  view ;  instead  of  which, 
our  guide  leads  by  narrow,  strange,  but  smooth  ways  to  a  small  emi- 
nence ;  he  has  finished !  He  lacks  the  calm  and  concentrated  energy 
for  a  deep  plunge  into  a  single  important  problem ;  and  in  this  way  the 
reader  also  hurries  with  inward  unrest  from  problem  to  problem,  as 
in  a  game  of  riddles,  without  being  able  to  enjoy  the  individual  one. 
Diophantus  dazzles  more  than  he  delights.  He  is  in  a  wonderful 
measure  shrewd,  clever,  quick-sighted,  indefatigable,  but  does  not 
penetrate  thoroughly  or  deeply  into  the  root  of  the  matter.  As  his 
problems  seem  framed  in  obedience  to  no  obvious  scientific  necessity, 
but  often  only  for  the  sake  of  the  solution,  the  solution  itself  also 
lacks  completeness  and  deeper  signification.  He  is  a  brilliant  performer 
in  the  art  of  indeterminate  analysis  invented  by  him,  but  the  science  has 


136  A  SHORT  HISTORY  OF  SCIENCE 

nevertheless  been  indebted,  at  least  directly,  to  this  brilliant  genius 
for  few  methods,  because  he  was  deficient  in  the  speculative  thought 
which  sees  in  the  True  more  than  the  Correct.  That  is  the  general 
impression  which  I  have  derived  from  a  thorough  and  repeated  study 
of  Diophantus  '  arithmetic.  —  Hankel. 

On  the  other  hand  Euler  remarks  :  — 

Diophantus  himself,  it  is  true,  gives  only  the  most  special  solu- 
tions of  all  the  questions  which  he  treats,  and  he  is  generally  content 
with  indicating  numbers  which  furnish  one  single  solution.  But  it 
must  not  be  supposed  that  his  method  was  restricted  to  these  very 
special  solutions.  In  his  time  the  use  of  letters  to  denote  undeter- 
mined numbers  was  not  yet  established,  and  consequently  the  more 
general  solutions  which  we  are  now  enabled  to  give  by  means  of  such 
notation  could  not  be  expected  from  him.  Nevertheless,  the  actual 
methods  which  he  uses  for  solving  any  of  his  problems  are  as  general 
as  those  which  are  in  use  to-day  ;  nay,  we  are  obliged  to  admit  that 
there  is  hardly  any  method  yet  invented  in  this  kind  of  analysis  of 
which  there  are  not  sufficiently  distinct  traces  to  be  discovered  in 
Diophantus. 

With  the  very  important  process  of  reducing  problems  to  equa- 
tions he  is  relatively  successful  and  often  highly  ingenious.  For 
example,  "to  find  three  niftnbers,  so  that  the  product  of  any  two  plus 
the  sum  of  the  same  two  shall  be  given  numbers,  for  example,  8,  15, 
and  24."  We  should  write  :  xy  +  x  +  y  =  8  ;  yz  +  y  +  z  =  15  ; 
zx  +  z+x-  =  24. 

Hence,  by  subtraction,  x(z  —  y)  +z  —  y  =16, 

Q 
,  z(x-y)  +x-y  =  9,z  +  1  =-  —  ,etc. 


z-y  x-y 

He,  on  the  other  hand,  takes  a  —  1  for  one  of  the  numbers  and 

9  16  12 

readily  obtains  --  1  and  --  1  for  the  others,  and  a  =  — 
a  a  5 

He  employs  tentative  assumptions  with  great  effect.  For 
example,  "  To  find  a  cube  and  its  root  such  that  if  the  same  number 
be  added  to  each,  the  sums  shall  also  be  a  cube  and  its  root."  If 


DECLINE  OF  ALEXANDRIAN  SCIENCE  137 

2x  is  the  original  number  and  x  the  number  added,  (an  arbitrary 
and  presumably  erroneous  assumption),  8z3  +  x  =  J27z3,  giving 
19z2  =  1.  The  coefficient  19  not  being  a  square,  he  now  seeks  to 
find  two  cubes  whose  difference  is  a  square.  If  (x  -+-  I)3  —  x*  is 
equated  to  (2x  —  I)2  the  special  solution  x  =  7  is  easily  obtained. 
Returning  to  the  original  problem,  the  new  assumption  is  made  :  — 
let  x  =  number  to  be  added,  7x  =  original  number. 

(7z)3  +  x  =  (&r)3  whence  x  =  ^ 

In  another  type  to  find  a  square  between  10  and  11,  he  multi- 
plies both  by  successive  squares  of  integers  until  between  the  prod- 
ucts (by  16)  he  finds  a  square,  169.  The  number  required  is 
10 A.  Such  processes  naturally  give  particular,  not  general, 
solutions. 

His  lost  Porisms  are  believed  to  have  "  contained  propositions 
in  the  theory  of  numbers  most  wonderful  for  the  time."  Sum- 
marizing his  methods  of  dealing  with  equations  we  may  say 
that :  - 

(1)  he  solves  completely  equations  of  the  first  degree  having 
positive  roots,  showing  remarkable  skill  in  reducing  simultaneous 
equations  to  a  single  equation  in  one  unknown ; 

(2)  he  has  a  general  method  for  equations  of  the  second  degree 
but  employs  it  only  to  find  one  positive  root  ; 

(3)  more  remarkable  than  his  actual  solutions  of  equations  are 
his  ingenious  methods  of  avoiding  equations  which  he  cannot  solve. 

How  far  his  work  was  original,  how  far  like  Euclid  in  his  Elements 
it  was  the  result  of  compilation,  cannot  be  definitely  ascertained. 
As  a  whole  it  is  somewhat  uneven  and  makes  rather  the  impression 
of  great  learning  than  of  exceptional  originality.  He  seems  in- 
debted in  part  to  predecessors  unknown  to  us.  For  him  the 
earlier  Greek  distinction  between  computation  and  arithmetic  has 
lost  its  force. 

In  reviewing  the  work  of  Pappus  and  Diophantus  Gow  says :  — 

the  Collections  of  Pappus  can  hardly  be  deemed  really  important.  .  .  . 
But  among  his  contemporaries,  Pappus  is  like  the  peak  of  Teneriffe  in 
the  Atlantic.  He  looks  back  from  a  distance  of  500  years,  to  find 


138  A  SHORT  HISTORY  OF  SCIENCE 

his  peer  in  Apollonius.  .  .  .  His  work  is  only  the  last  convulsive  effort 
of  Greek  geometry,  which  was  now  nearly  dead,  and  was  never  effec- 
tually revived.  ...  It  is  not  so  with  Ptolemy  or  Diophantus.  The 
trigonometry  of  the  former  is  the  foundation  of  a  new  study  which  was 
handed  on  to  other  nations,  indeed,  but  which  has  thenceforth  a  con- 
tinuous history  of  progress.  Diophantus  also  represents  the  outbreak 
of  a  movement  which  probably  was  not  Greek  in  its  origin,  and  which 
the  Greek  genius  long  resisted,  but  which  was  especially  adapted  to 
the  tastes  of  the  people  who,  after  the  extinction  of  Greek  schools, 
received  their  heritage  and  kept  their  memory  green.  But  no  Indian 
or  Arab  ever  studied  Pappus  or  cared  in  the  least  for  his  style  or  his 
matter.  When  geometry  came  once  more  up  to  his  level,  the  inven- 
tion of  analytical  methods  gave  it  a  sudden  push  which  sent  it  far 
beyond  him  and  he  was  out  of  date  at  the  very  moment  when  he  seemed 
to  be  taking  a  new  lease  of  life. 

A  melancholy  interest  attaches  to  the  fate  of  Hypatia,  daughter 
of  Theon  an  Alexandrian  mathematician,  herself  a  teacher  of 
Greek  philosophy  and  mathematics,  who  was  torn  to  pieces  by 
a  Christian  mob,  doubtless  as  a  representative  of  pagan  (Greek) 
learning,  at  Alexandria  in  415  A.D. 

CONCLUSION  AND  RETROSPECT.  —  Intellectual  interests  in  the 
Greek  world  (now  really  Roman)  were  by  this  time  so  completely 
alienated  from  mathematics,  and  indeed  from  science  in  general, 
that  the  brilliant  work  of  Pappus  and  Diophantus  aroused  but 
slight  and  temporary  interest.  Geometry  had  reached  within  the 
possible  range  of  the  Euclidean  method  a  relatively  complete 
development.  Algebra  under  Diophantus  attained  in  spite  of 
hampering  notation  a  level  not  again  approached  for  many  cen- 
turies. 

Little  need  be  said  of  sciences  other  than  those  already  dealt 
with.  These,  even  more  than  mathematics  and  astronomy,  shrank 
under  Roman  autocracy  and  Christian  hostility.  Only  the 
works  of  Galen,  Strabo,  and  Pliny  need  be  mentioned,  and  with 
them  we  deal  in  the  next  chapter. 

The  torch  of  science  now  passes  from  the  Greeks  to  the  Indians 
of  the  far  East  after  their  conquest  by  Alexander,  to  be  in  turn 


DECLINE  OF  ALEXANDRIAN  SCIENCE  139 

surrendered  to  the  Mohammedan  conquerors  of  Alexandria  A.D. 
641.  By  them  it  is  kept  from  extinction  until  in  later  ages  it  is 
once  more  fanned  to  ever  increasing  radiance  in  western  Europe. 
In  attempting  a  retrospective  estimate  of  Greek  science  it  is 
fundamentally  important  to  judge  the  whole  background  fairly. 
In  science  the  Greeks  had  to  build  from  the  foundations.  Other 
peoples  had  extensive  knowledge  and  highly  developed  arts.  Only 
among  the  Greeks  existed  the  true  scientific  method  with  its  char- 
acteristics of  free  inquiry,  rational  interpretation,  verification  or 
rectification  by  systematic  and  repeated  observation,  and  con- 
trolled deduction  from  accepted  principles. 

The  Assyrians,  Babylonians  and  Egyptians  had  certainly  made 
great  progress  in  the  use  of  mechanical  devices  for  moving  heavy  loads, 
in  the  construction  of  scales,  and  of  pumps.  Their  measuring  in- 
struments were  well  developed,  and  acute  observations  were  made, 
but  of  systematic,  scientific  investigation  there  is  no  evidence.  The 
Greeks  received  many  results  and  suggestions  from  Asia  Minor,  Meso- 
potamia, and  Egypt,  but  their  achievements  are  essentially  their  own. 

—  Wiedemann. 

In  asking  ourselves  why  these  extraordinary  beginnings  seemed 
after  a  time  to  lose  their  power  of  continued  development,  we  must 
not  forget  the  effect  of  external  conditions.  It  is  conceivable 
indeed  that  scientific  progress  should  continue  from  age  to  age, 
through  the  genius  of  individual  teachers  and  students,  regardless 
of  political  and  social  conditions.  Such,  however,  is  not  the 
historic  fact.  For  progress  in  science  men  of  genius  are  indis- 
pensable, but  in  no  country  or  age  have  they  alone  been  able  to 
make  science  flourish  under  conditions  so  unfavorable  as  were 
those  of  the  early  centuries  of  the  Christian  era. 

Greek  science,  however,  did  not  "  fail,"  learned  and  elaborate 
as  are  the  explanations  that  have  been  given  of  its  alleged  failure. 
Under  "the  chill  breath  of  Roman  autocracy"  its  growth  was  in- 
deed checked,  its  animation  suspended,  for  a  full  thousand  years. 
Then  in  the  Renaissance  it  renewed  its  vitality  and  has  ever  since 
been  advancing  more  and  more  magnificently.  This  is  not  to  say 


140  A  SHORT  HISTORY  OF  SCIENCE 

that  criticisms  as  to  the  imperfections  of  the  Greek  scientific 
method  are  invalid,  but  rather  to  assert,  as  most  critics  must  agree, 
that  its  merits  outweighed  its  defects,  and  that  the  latter  would 
not  have  proved  disastrous  but  for  the  development  of  political, 
economic  and  military  conditions  under  which  the  free  Greek  spirit 
could  not  continue  its  wonderful  achievements. 

REFEBENCES  FOR  READING 

BALL.    Chapters  IV,  V. 

BERRY.     Chapter  II,  Articles  37-54. 

DREYER.     Chapters  VI-IX. 

Gow.    Chapters  IV,  VIII,  IX,  X. 

HEATH.    Diophantus  of  Alexandria.    Aristarchus  of  Samos. 


CHAPTER  VII 
THE  ROMAN  WORLD.    THE  DARK  AGES 

Among  them  [the  Greeks]  Geometry  was  held  in  highest  honor : 
nothing  was  more  glorious  than  Mathematics.  But  we  have  limited 
the  usefulness  of  this  art  to  measuring  and  calculating.  —  Cicero. 

The  Romans  were  as  arbitrary  and  loose  in  their  ideas  as  the 
Greeks,  without  possessing  their  invention,  acuteness  and  spirit  of 
system.  —  Whewell. 

The  Romans,  with  their  limited  peasant  horizon  and  their  short- 
sighted practical  simplicity,  cherished  always  for  true  science  in  their 
inmost  hearts  that  peculiar  mixture  of  suspicion  and  contempt  which 
is  so  familiar  today  among  the  half  educated.  The  arch  dilettante 
Cicero  boasts,  even,  that  his  countrymen,  thank  God !  are  not  like 
those  Greeks,  but  confine  the  study  of  mathematics  and  that  sort  of 
thing  to  the  practically  useful.  —  Heiberg. 

THE  ROMAN  WORLD-EMPIRE.  —  For  several  centuries,  during 
the  decline  of  Greek  learning  both  in  Greece  itself  and  in  Alexan- 
dria, two  new  and  powerful  States  were  developing ;  one  having  its 
centre  at  Carthage  on  the  northern  shore  of  Africa,  almost  opposite 
Sicily,  the  other — the  Roman  Empire  —  on  the  western  shore  of 
Italy  in  the  valley  of  the  Tiber.  The  latter,  at  first  comparatively 
insignificant,  rapidly  rose  to  a  position  of  world-wide  power,  con- 
quering in  turn  Carthage,  Greece,  and  the  East  and  eventually 
extending  over  the  greater  part  of  the  then  known  world,  from 
Britain  on  the  north  to  the  Cataracts  of  the  Nile  on  the  south, 
from  India  in  the  east  to  the  Pillars  of  Hercules  in  the  west. 

THE  ROMAN  ATTITUDE  TOWARDS  SCIENCE.  —  One  of  the  most 
striking  facts  in  the  history  of  science  is  the  total  lack  of  any 
evidence  of  real  interest  in  science  or  in  scientific  research  among 
the  Roman  people  itself  or  any  people  under  Roman  sway.  Alex- 
andrian science,  even,  though  previously  flourishing,  languished 
and  went  steadily  to  its  fall  after  the  submission  of  that  city  to 
the  Romans  in  the  first  century  B.C.  The  truth  seems  to  be  that 

141 


142  A  SHORT  HISTORY  OF  SCIENCE 

the  Roman  people,  while  highly  gifted  in  oratory,  literature,  and 
history  (as  witness,  for  example,  the  works  of  Cicero,  Virgil  and 
Tacitus),  were  not  interested  and  therefore  not  successful  in  scien- 
tific work.  This  is  the  more  impressive  when  we  reflect  upon  their 
marvellous  military  genius,  and  their  preeminence  in  world-wide 
power,  dominion  and  influence.  In  vain  do  we  look  for  any  Roman 
scientist  or  philosopher  of  such  originality  or  range  as  Aristotle  or 
Plato ;  for  any  Roman  astronomer,  like  Aristarchus  or  Hipparchus 
or  Ptolemy;  for  any  Roman  mathematician  or  inventor,  like 
Archimedes;  for  any  Roman  natural  philosopher,  like  Democ- 
ritus ;  for  any  Roman  pioneer  in  medicine,  like  Hippocrates,  — 
for  Galen  was  Roman  neither  by  birth  nor  education,  but  only 
by  adoption  late  in  life. 

ROMAN  ENGINEERING  AND  ARCHITECTURE.  —  There  is  how- 
ever one  marked  feature  of  Roman  civilization  in  which  extraor- 
dinary ability  was  displayed  and  peculiar  excellence  achieved 
and  in  which  the  Romans  were  unquestionably  far  superior  to  all 
their  predecessors  and,  until  very  recent  times,  to  all  their  suc- 
cessors. This  feature,  which  is  one  of  the  most  characteristic,  is 
the  Roman  genius  for  both  military  and  civil  engineering.  It  is 
only  necessary  to  mention  the  surviving  remains  of  Roman  walls, 
fortresses,  roads,  aqueducts,  theatres,  baths,  and  bridges.  Never 
before  and  never  since  has  any  empire  built  so  many,  so  splendid, 
and  so  enduring  monuments  for  the  service  of  its  peoples  in  peace 
and  in  war.  The  surface  of  southern  Europe,  western  Asia  and 
northern  Africa  is  still  covered  after  the  lapse  of  twenty  centuries 
with  Roman  remains  which  bid  fair  to  resist  decay  and  destruc- 
tion for  another  two  thousand  years.  Roman  engineering  is  almost 
as  distinguished  as  is  Roman  law.  The  Emperor  Constantine 
in  the  fourth  century  wrote :  "  We  need  as  many  engineers  as  pos- 
sible. As  there  is  lack  of  them,  invite  to  this  study  persons  of  about 
18  years,  who  have  already  studied  the  necessary  sciences.  Re- 
lieve the  parents  of  taxes  and  grant  the  scholars  sufficient  means." 
The  land  surveyors  formed  a  well-organized  gild,  but  they  were 
merely  practitioners  of  a  traditional  art,  perpetuating  the  errors 
of  their  ancient  Egyptian  predecessors,  not  dreaming  of  new  dis- 


THE  ROMAN  WORLD  143 

coveries,  nor  even  of  imparting  such  knowledge  as  they  had,  — 
outside  the  ranks  of  their  own  gild. 

SLAVE  LABOR  IN  ANTIQUITY.  —  It  must  never  be  forgotten 
that  throughout  antiquity,  and  to  a  great  extent  even  until  very 
recent  times,  the  labor  question  was  wholly  different  from  what 
it  is  to-day.  Instead  of  the  labor-saving  machinery  which  is  so 
extraordinary  a  feature  of  our  time,  but  which  was  practically  non- 
existent before  the  end  of  the  eighteenth  century,  the  slave  was  the 
machine  for  all  heavy  labor.  It  is  not  likely  that  he  was  ever  a 
particularly  cheap  machine,  but  in  the  mass  he  was  powerful,  and 
it  was  probably  largely  by  his  labor  that  the  fields  were  cultivated 
and  irrigated,  and  that  dams  and  ditches,  walls  and  towers,  roads 
and  bridges  and  pyramids  and  temples,  were  built  and  fortified. 
It  is  notorious  that  the  so-called  "ships"  of  war,  the  galleys, 
were  manned  by  slaves,  even  down  to  modern  times.  It  is  difficult 
to  determine  the  efficiency  of  labor  of  this  kind  because  we  are 
generally  ignorant  as  to  the  time  factor,  but  whether  from  our 
modern  point  of  view  inefficient  or  not,  the  results  were  often  re- 
markable and  sometimes,  as  in  the  case  of  the  Pyramids,  stupendous. 

JULIUS    CAESAR   AND    THE     JULIAN     CALENDAR.  —  Julius    Csesar 

himself  undertook  two  great  problems  of  practical  mathematical 
science :  —  the  rectification  of  the  highly  confused  calendar,  and 
a  survey  of  the  whole  Roman  empire.  In  the  year  47  B.C.  the 
accumulated  calendar  error  amounted  to  not  less  than  85  days. 
Reform  was  accomplished  by  a  decree  making  the  year  con- 
sist of  365  days  with  an  additional  day  in  February  once  in  four 
years.  The  survey,  of  which  the  results  were  to  be  shown  in  a 
great  fresco  map,  was  not  carried  out  until  the  reign  of  Augustus. 
VITRUVIUS  ON  ARCHITECTURE.  —  The  most  famous  ancient  work 
on  building  and  kindred  topics,  including  building  materials,  is 
that  entitled  De  Architectura,  by  Vitruvius,  a  Roman  architect 
and  engineer  living  (about  14  B.C.)  in  the  age  of  Augustus.  This 
celebrated  work  was  the  only  one  of  importance  on  architecture 
known  to  the  Middle  Ages,  and  was  the  guide  and  text-book  of 
the  builders  of  that  period  as  well  as  of  those  of  the  Renaissance. 
The  book  (now  easily  accessible  in  translation)  is  in  part  a 


144  A  SHORT  HISTORY  OF  SCIENCE 

compilation  from  earlier,  and  especially  Greek,  authors,  and  in 
part  original.  Vitruvius  uses  for  TT  the  value  3 J,  —  less  ac- 
curate than  that  of  Archimedes,  but  displaced  later  by  the  crude 
approximation  3.  Of  Vitruvius's  life  and  work  almost  nothing  is 
known,  but  no  other  ancient  treatise  of  a  similar  technical  nature 
has  had  in  its  own  field  so  much  influence  on  posterity. 

FRONTINUS  ON  THE  WATERWORKS  OF  ROME  (c.  40-103  A.D.). 
At  about  the  end  of  the  first  century  of  our  era,  Sextus  Julius 
Frontinus,  a  Roman  soldier  and  engineer,  wrote  a  highly  interest- 
ing and  valuable  account  of  the  waterworks  of  Rome.  Frontinus 
served  as  prcetor  under  Vespasian ;  was  afterwards  sent  to  Britain 
as  Roman  governor  of  that  island ;  was  superseded  by  Agricola  in 
78  A.D.  and  was  appointed  in  97  A.D.  Curator  Aquarum,  "  an  office 
never  conferred  except  upon  persons  of  very  high  standing." 

ROMAN  NATURAL  SCIENCE  AND  MEDICINE.  —  Among  the  Roman 
workers  and  authors  of  importance  in  the  history  of  natural  science 
and  medicine  only  a  few  require  more  than  passing  notice.  This 
is  the  more  remarkable  when  we  reflect  upon  the  vast  extension  of 
the  Roman  empire  and  the  novel  and  hitherto  unequalled  op- 
portunities afforded  for  observation  and  collection  in  natural 
history,  and  for  the  study  of  anthropology,  geography,  geology, 
meteorology,  climatology,  zoology,  botany  and  the  like,  —  not  to 
mention  military  surgery,  and  the  hygiene  and  sanitation  of  camp- 
life. 

LUCRETIUS  (98-55  B.C.)  is  to-day  regarded  not  only  as  a  great 
Roman  poet  but  also  as  the  most  perfect  exponent  in  his  time  of 
the  natural  philosophy  of  the  Greeks  who  preceded  him.  He  was 
a  contemporary  and  a  few  years  the  junior  of  Cicero  and  Julius 
Caesar.  The  first  two  books  and  the  fifth  of  his  De  Rerum 
Natura  (On  the  Nature  of  Things)  are  of  interest  to  the  modern 
scientific  student,  because  of  their  dealing  with  problems  of  per- 
manent importance  to  mankind.  He  was  a  disciple  of  Epicurus, 
and  apparently  also  well  acquainted  with  the  works  of  Empedocles, 
Democritus,  Anaxagoras,  and  many  other  of  the  great  Greek  writers 
such  as  Homer,  Hippocrates,  Thucydides,  and  especially  Euripides. 
The  title  of  his  famous  poem  shows  his  interest  in  natural  philos- 


THE  ROMAN  WORLD  145 

ophy,  and  there  is  evidence  that  he  was  also  a  teacher  and  re- 
former.    He  is  antagonistic  to  superstition  and  a  strong  advocate 
of  rationalism,  but  he  is  neither  irreverent  nor  revolutionary. 
The  following  passages  are  typical :  — 

Water  in  summer  time  flows  cool  in  wells, 
Because  the  Earth  then  rarefied  by  heat, 
Its  proper  stores  most  radiate  to  the  air. 
Hence  more  the  Earth  is  drained  of  its  heat, 
And  colder  grow  the  currents  under  ground. 
But  when  by  cold  in  winter  'tis  compressed, 
Its  heat  escaping  passes  into  wells.  .  .  . 

And  now  to  tell  by  which  of  Nature's  laws, 

The  stone  called  Magnet  by  the  Greeks,  —  since  first 

'Mong  the  Magnesians  found,  —  can  iron  draw. 

Men  gaze  with  wonder  on  the  marvellous  stone, 

With  pendent  chain  of  rings,  oft  five  or  more, 

Light  hanging  in  the  air  suspensive,  while 

One  from  another  feels  the  influence  of  the  stone 

That  sends  through  all  its  wonder-working  power. 

Here  many  principles  we  must  first  lay  down 

And  slow  approach  by  long  preparative, 

Rightly  to  solve  the  rare  phenomenon. 

The  more  exact  I  then  attentive  ears.  .  .  . 

How  different  is  fire  from  piercing  frost ! 

Yet  both  composed  of  atoms  toothed  and  sharp, 

As  proved  by  touch.     Touch,  O  ye  sacred  powers  — 

Touch  is  the  organ  whence  all  knowledge  flows ; 

Touch  is  the  body's  sense  of  things  extern, 

And  of  sensations  that  deep  spring  within ; 

Whether  delightsome,  as  in  genial  act, 

Or  rude  collision  torturing  from  without ; 

How  different,  then,  must  forms  of  atoms  be 

Which  such  sensation  varied  can  produce ! 

STRABO, — a  Roman  traveller,  historian  and  geographer,  lived 
somewhere  between  63  B.C.  and  24  A.D.  His  Geography  is  the 
most  important  work  on  that  subject  surviving  from  antiquity  and, 


146  A  SHORT  HISTORY  OF  SCIENCE 

while  apparently  building  on  the  foundation  laid  by  Eratosthenes, 
is  plainly  an  original  work  devoted  largely  to  his  own  explorations 
and  observations  during  years  of  travel  and  study  in  different 
countries,  including  Italy,  Greece,  Asia  Minor,  Egypt,  and  Ethiopia. 
He  himself  says :  — 

Westward  I  have  journeyed  to  the  parts  of  Etruria  opposite  Sar- 
dinia ;  towards  the  South  from  the  Euxine  to  the  borders  of  Ethiopia, 
and  perhaps  not  one  of  those  who  have  written  geographies  has 
visited  more  places  than  I  have  between  those  limits. 

His  work  is  invaluable  as  a  picture  of  the  limited  geographical 
knowledge  of  the  time,  but  he  had  no  such  mathematical  knowledge 
of  geography  as  had  his  great  predecessors,  Eratosthenes,  Hip- 
parchus,  and  Ptolemy. 

PLINY  THE  ELDER  (23-79  A.D.),  sometimes  called  Pliny  the 
Naturalist,  is  another  Roman  of  scientific  attainments,  whose  great 
work  entitled  Natural  History,  although  more  an  encyclopaedia  of 
miscellaneous  information  than  a  scientific  treatise,  is,  nevertheless, 
like  the  works  of  Herodotus,  a  landmark  in  the  history  of  civil- 
ization. It  consists  of  thirty-seven  books  and  is  easily  accessible 
in  English.  Pliny  deals  with  the  universe,  God,  nature,  and 
natural  phenomena ;  with  earth,  stars,  earthquakes ;  with  man, 
beasts,  shells,  fishes,  insects,  trees,  fruits,  gums,  perfumes,  timber, 
the  diseases  of  plants,  metals,  stones,  precious  stones,  etc.  The 
author  met  his  death  in  that  eruption  of  Vesuvius  which  over- 
whelmed Pompeii  in  79  A. D.  and  because  of  his  scientific  curiosity 
which  led  him  to  approach  too  near  to  the  volcano. 

GALEN  (CLAUDIUS  GALENUS)  who  flourished  in  the  second 
century  A.D.  was  born  and  partly  educated  at  Pergamum  in  Asia 
Minor,  where,  after  much  travelling,  and  research,  chiefly  in 
anatomy  and  philosophy  at  Smyrna  and  at  Alexandria,  he  also 
practised  the  healing  art.  Sent  for  by  the  Roman  emperor,  Lucius 
Verus,  he  was  afterward  physician  to  Marcus  Aurelius  and  his 
son  Commodus.  His  writings  are  voluminous,  encyclopedic  and 
anatomically  important,  though  not  especially  original,  and  his 
name  is  often  linked  with  that  of  Hippocrates,  partly,  no  doubt, 


THE  ROMAN  WORLD  147 

because  after  Galen  we  find  no  great  name  in  anatomy  until  we 
come  to  Vesalius,  some  1400  years  later. 

LATE  ROMAN  MATHEMATICAL  SCIENCE.  —  Two  periods  may  be 
distinguished  in  ancient  mathematical  science,  the  first  beginning 
with  Pythagoras  and  ending  with  Hero.  To  these  four  to  five 
centuries  belong  all  the  original  works  in  geometry,  astronomy, 
mechanics,  and  music.  The  period  closes  with  the  extension  of 
the  pax  Romano,  over  the  Orient.  The  second  extends  to  the 
sixth  century,  when  Hellenism  is  proscribed  by  the  new  religion, 
the  genius  of  invention  is  extinct,  and  men  merely  study  the  older 
works,  commenting  and  coordinating.  Astronomy  gradually 
reverts  to  astrology,  the  mathematical  geography  well  begun 
under  Eratosthenes  and  Ptolemy  becomes  superficial  and  descrip- 
tive, with  Strabo  and  even  with  Posidonius. 

Whatever  the  eminence  of  the  Romans  in  the  practical  arts  of 
war,  politics  and  engineering,  their  interest  in  abstract  science 
was  almost  nil.  On  the  other  hand,  commercial  arithmetic, 
which  had  been  studiously  neglected  by  Greek  mathematicians, 
now  had  the  place  of  honor.  The  Roman  numerals,  clumsy  as 
they  seem  to  us,  were  superior  to  the  Greek,  and  a  useful  system 
of  finger-reckoning  was  developed,  supplementing  the  skilful  use 
of  the  abacus.  If  no  abacus  was  at  hand,  the  corresponding  lines 
were  quickly  traced  on  sand  or  dust,  small  stones  or  calculi  — 
whence  our  words  calculation  and  calculus,  —  serving  as  counters. 
A  complete  Roman  abacus  —  of  which  no  example  has  come  down 
to  us  —  seems  to  have  had  eight  long  and  eight  short  grooves.  Of 
the  former,  one  held  five  counters  or  buttons,  each  of  the  others 
four,  each  of  the  short  grooves  one,  these  last  counting  as  five 
units  each.  The  grooves  with  six  counters  served  for  computa- 
tions with  fractions.  Geometry  —  but  of  Hero  rather  than  of 
Euclid  —  was  valued  for  its  utility  in  surveying  and  architecture. 
Preparation  for  the  engineering  art  included  mathematics,  optics, 
astronomy,  history,  and  law.  There  were  also  teachers  of  me- 
chanics and  architecture.  (See  Vitruvius,  above.) 

CAPELLA.  —  Early  in  the  fifth  century  Martianus  Capella  wrote 
a  compendium  of  grammar,  dialectics,  rhetoric,  geometry,  arith- 


148  A  SHORT  HISTORY  OF  SCIENCE 

metic,  music,  and  astronomy,  of  great  and  lasting  educational 
influence.  His  classification  of  these  "seven  liberal  arts"  main- 
tained itself  throughout  the  Middle  Ages  and  is  not  yet  wholly 
extinct.  Gregory  of  Tours  for  example  says:  —  "If  thou  wilt 
be  a  priest  of  God,  then  let  our  Martianus  instruct  thee  first  in 
the  seven  sciences." 

BOETHIUS  (480-524)  born  at  Rome  on  the  eve  of  its  fall  in  476 
is  the  author  not  only  of  the  famous  Consolations  of  Philosophy 
but  also  of  works  on  Music  and  on  Arithmetic  which  long  served 
to  represent  Greek  mathematics  to  the  medieval  world.  In  the 
course  of  his  public-spirited  career,  Boethius  interested  himself 
in  the  reform  of  the  coinage  and  in  the  introduction  of  water- 
clocks  and  sun-dials.  His  geometry  consists  merely  of  some  of 
the  simpler  propositions  of  Euclid,  with  proofs  of  the  first  three 
only,  and  with  applications  to  mensuration.  Yet  the  intellectual 
poverty  of  the  age  was  such  that  this  remained  long  the  standard 
for  mathematical  teaching.  Boethius'  Arithmetic  begins :  — 

By  all  men  of  old  reputation  who  following  Pythagoras'  reputation 
have  distinguished  themselves  by  pure  intellect  it  has  always  been 
considered  settled  that  no  one  can  reach  the  highest  perfection  of 
philosophical  doctrines,  who  does  not  seek  the  height  of  learning  at 
a  certain  crossway  —  the  quadrivium. 

For  him  the  things  of  the  world  are  either  discrete  (multitudes), 
or  continuous  (magnitudes).  Multitudes  are  represented  by 
numbers,  or  in  their  ratios  by  music;  magnitudes  at  rest  are 
treated  by  geometry,  those  in  motion  by  astronomy.  These  four 
of  the  seven  liberal  arts  form  the  quadrivium;  grammar,  dialec- 
tics and  rhetoric,  the  trivium.  A  Christian  in  faith,  a  pagan  in 
culture,  Boethius  has  been  called  the  "  bridge  from  antiquity  to 
modern  times."  (See  page  50.) 

The  scholars  of  the  time  were  almost  without  exception  men 
whose  first  interests  were  theological.  Mathematics,  having  no 
direct  moral  significance,  seemed  to  them  in  itself  unworthy  of 
attention.  On  the  other  hand,  they  attached  exaggerated  im- 
portance to  all  sorts  of  mystical  attributes  of  numbers  and  to  the 


THE  DARK  AGES  149 

interpretation  of  scriptural  numbers.  Thus  Augustine  says  the 
science  of  numbers  is  not  created  by  men,  but  merely  discovered, 
residing  in  the  nature  of  things. 

Whether  numbers  are  regarded  by  themselves  or  their  laws  applied 
to  figures,  lines  or  other  motions,  they  have  always  fixed  rules,  which 
have  not  been  made  by  men  at  all,  but  only  recognized  by  the  keen- 
ness of  shrewd  people. 

SCIENCE  AND  THE  EARLY  CHRISTIAN  CHURCH.  —  In  the  earlier 
centuries  of  our  era  the  history  of  science  gradually  enters  upon 
a  new  phase.  The  more  highly  developed  civilization  of  Greece 
and  Rome,  weakened  by  corruption,  has  finally  yielded  to  the 
attacks  on  the  one  hand  of  barbarous  or  semicivilized  races,  — 
Goths,  Vandals,  Huns,  and  Arabs,  —  and  on  the  other  hand 
to  a  moral  revolution  of  humble  Jewish  origin.  These  changes 
were  adverse  to  the  development,  or  even  the  survival,  of  Greek 
science.  The  destructive  relation  of  the  northern  barbarians  to 
scientific  progress  may  be  easily  imagined.  The  policy  of  official 
Christianity  was  based  on  antecedent  antipathy  for  the  unmoral 
intellectual  attitude  and  the  degenerate  character  which  the  early 
Christians  found  in  close  association  with  Greek  learning,  and  on 
a  too  literal  interpretation  of  the  Jewish  scriptures,  with  their 
primitive  Chaldean  theories  of  cosmogony  and  the  world. 

Justin  Martyr,  in  the  second  century,  says  that  what  is  true 
in  the  Greek  philosophy  can  be  learned  much  better  from  the 
Prophets.  Clement  of  Alexandria  (d.  227)  calls  the  Greek  philoso- 
phers robbers  and  thieves  who  have  given,  out  as  their  own  what 
they  have  taken  from  the  Hebrew  prophets.  Tertullian  (160-220) 
insists  that  since  Jesus  Christ  and  his  gospel,  scientific  research 
has  become  superfluous.  Isidore  of  Seville  in  the  seventh  century 
declares  it  wrong  for  a  Christian  to  occupy  himself  with  heathen 
books,  since  the  more  one  devotes  himself  to  secular  learning,  the 
more  is  pride  developed  in  his  soul.  Lactantius  early  in  the 
'fourth  century  includes  in  his  "Divine  Institutions"  a  section, 

'  On  the  false  wisdom  of  the  philosophers/  of  which  the  24th  chap- 
ter is  devoted  to  heaping  ridicule  on  the  doctrine  of  the  spherical 


150  A  SHORT  HISTORY  OF  SCIENCE 

figure  of  the  earth  and  the  existence  of  antipodes.  It  is  unnecessary 
to  enter  into  particulars  as  to  his  remarks  about  the  absurdity  of  be- 
lieving that  there  are  people  whose  feet  are  above  their  heads,  and 
places  where  rain  and  hail  and  snow  fall  upwards,  while  the  wonder 
of  the  hanging  gardens  dwindles  into  nothing  when  compared  with 
the  fields,  seas,  towns,  and  mountains,  supposed  by  philosophers  to 
be  hanging  without  support.  He  brushes  aside  the  argument  of 
philosophers  that  heavy  bodies  seek  the  centre  of  the  earth,  as  un- 
worthy of  serious  notice ;  and  he  adds  that  he  could  easily  prove  by 
many  arguments  that  it  is  impossible  for  the  heavens  to  be  lower  than 
the  earth,  but  he  refrains  because  he  has  nearly  come  to  the  end  of  his 
book,  and  it  is  sufficient  to  have  counted  up  some  errors,  from  which 
the  quality  of  the  rest  may  be  imagined. 

It  was  natural  that  Augustine  (354-430),  .  .  .  should  express  him- 
self with  .  .  .  moderation,  as  befitted  a  man  who  had  been  a 
student  of  Plato  as  well  as  of  St.  Paul  in  his  younger  days.  With 
regard  to  antipodes,  he  says  that  there  is  no  historical  evidence  of 
their  existence,  but  people  merely  conclude  that  the  opposite  side  of 
the  earth,  which  is  suspended  in  the  convexity  of  heaven,  cannot  be 
devoid  of  inhabitants.  But  even  if  the  earth  is  a  sphere,  it  does  not 
follow  that  that  part  is  above  water,  or,  even  if  this  be  the  case,  that 
it  is  inhabited ;  and  it  is  too  absurd  to  imagine  that  people  from  our 
parts  could  have  navigated  over  the  immense  ocean  to  the  other 
side,  or  that  people  over  there  could  have  sprung  from  Adam.  With 
regard  to  the  heavens,  Augustine  was,  like  his  predecessors,  bound 
hand  and  foot  by  the  unfortunate  water  above  the  firmament.  He 
says  that  those  who  defend  the  existence  of  this  water  point  to 
Saturn  being  the  coolest  planet,  though  we  might  expect  it  to  be 
much  hotter  than  the  sun,  because  it  travels  every  day  through  a 
much  greater  orbit ;  but  it  is  kept  cool  by  the  water  above  it.  The 
water  may  be  in  a  state  of  vapor,  but  in  any  case  we  must  not 
doubt  that  it  is  there,  for  the  authority  of  Scripture  is  greater  than 
the  capacity  of  the  human  mind.  He  devotes  a  special  chapter  to 
the  figure  of  the  heaven,  but  does  not  commit  himself  in  any  way 
though  he  seems  to  think  that  the  allusions  in  Scripture  to  the  heaven 
above  us  cannot  be  explained  away  by  those  who  believe  the  world 
to  be  spherical.  But  anyhow  Augustine  did  not,  like  Lactantius, 
treat  Greek  science  with  ignorant  contempt;  he  appears  to  have 
had  a  wish  to  yield  to  it  whenever  Scripture  did  not  pull  him  the 


THE  DARK  AGES  151 

other  way,  and  in  times  of  bigotry  and  ignorance  this  is  deserving 
of  credit.  —  Dreyer. 

Arguing  elsewhere  that  the  soul  perceives  what  the  bodily  eye 
cannot,  Augustine  avails  himself  of  the  geometrical  analogy  of 
the  ideal  straight  line  which  shall  have  length  without  breadth  or 
thickness,  but  he  lapses  into  mysticism  when  he  passes  to  the 
circle. 

The  biographer  of  St.  Eligius  (writing  in  760  under  Pepin)  says 
'What  do  we  want  with  the  so-called  philosophies  of  Pythagoras, 
Socrates,  Plato  and  Aristotle,  or  with  the  rubbish  and  nonsense  of 
such  shameless  poets  as  Homer,  Virgil  and  Menander  ?  What  serv- 
ice can  be  rendered  to  the  servants  of  God  by  the  writings  of  the 
heathen  Sallust,  Herodotus,  Livy,  Demosthenes  or  Cicero  ?'  Frede- 
gar  .  .  .  complains  (about  600)  that '  The  world  is  in  its  decrepitude, 
intellectual  activity  is  dead,  and  the  ancient  writers  have  no  suc- 
cessors/ .  .  .  —  G.  H.  Putnam,  Books  of  the  Middle  Ages. 

The  following  is  a  broad  survey  of  the  whole  period :  — 

The  soft  autumnal  calm  .  .  .  which  lingered  up  to  the  Antonines 
over  that  wide  expanse  of  empire  from  the  Persian  Gulf  to  the  Pillars 
of  Hercules  and  from  the  Nile  to  the  Clyde  .  .  .  was  only  a  misleading 
transition  to  that  bitter  winter  which  filled  the  half  of  the  second 
and  the  whole  of  the  third  century,  to  be  soon  followed  by  the  abiding 
dark  and  cold  of  the  Middle  Ages.  The  Empire  was  moribund  when 
Christianity  arose.  Rome  had  practically  slain  the  ancient  world 
before  the  Empire  replaced  the  Republic.  The  barbarous  Roman 
soldier  who  killed  Archimedes  absorbed  in  a  problem,  is  but  an  in- 
stance and  a  type  of  what  Rome  had  done  always  and  everywhere  by 
Greek  art,  civilization  and  science.  The  Empire  lived  upon  and  con- 
sumed the  capital  of  preceding  ages,  which  it  did  not  replace.  Popu- 
lation, production,  knowledge,  all  declined  and  slowly  died.  .  .  . 

The  sun  of  ancient  science,  which  had  risen  in  such  splendour 
from  Thales  to  Hipparchus,  was  now  sinking  rapidly  to  the  horizon ; 
and  when  it  at  last  disappeared,  say,  in  the  fifth  century,  the  long 
night  of  the  Middle  Ages  began.  .  .  .  The  pursuit  of  knowledge  for 
knowledge's  sake  was  out  of  place.  .  .  .  All  the  outlets  through 
which  modern  energy  is  chiefly  expended  were  then  closed ;  a  man 
could  not  serve  the  state  as  a  citizen,  he  could  not  serve  knowledge 


152  A  SHORT  HISTORY  OF  SCIENCE 

as  a  man  of  science.  .  .  .  There  was  only  one  thing  left  for  him  to 
do,  —  to  serve  God.  —  J.  C.  Morison,  The  Service  of  Man. 

THE  EASTERN  EMPIRE.  EDICT  OP  JUSTINIAN.  —  Only  half  a 
century  after  the  fall  of  Rome  the  Greek  schools  in  Athens  were 
closed,  in  529  A.D.,  by  order  of  the  emperor  Justinian,  and  intel- 
lectual darkness  settled  down  over  Eastern  Europe.  Theology 
became  more  than  ever  the  chief  pursuit  of  the  educated,  and  Greek 
learning  more  than  ever  neglected.  Many  Greek  manuscripts, 
however,  were  hidden  away,  and  many  Greek  scholars,  though 
scattered,  kept  alive  the  feeble  spark  of  Greek  learning. 

THE  DARK  AGES.  —  After  the  mighty  Roman  Empire  of  the 
West  had  come  to  its  end,  the  peoples  of  Christian  Europe  and  of 

the  Graeco-Roman  world  descended  into  the  great  hollow  which  is 
roughly  called  the  Middle  Ages,  extending  from  the  fifth  to  the  fifteenth 
century,  a  hollow  in  which  many  great  and  beautiful  and  heroic  things 
were  done  and  created,  but  in  which  knowledge,  as  we  understand  it 
and  as  Aristotle  understood  it,  had  no  place.  The  revival  of  learning 
and  the  Renaissance  are  memorable  as  the  first  sturdy  breasting  by 
humanity  of  the  hither  slope  of  that  great  hollow  which  lies  between 
us  and  the  ancient  world.  The  modern  man,  reformed  and  regenerated 
by  knowledge,  looks  across  it  and  recognizes  on  the  opposite  ridge,  in 
the  far-shining  cities  and  stately  porticoes,  in  the  art,  politics  and 
science  of  antiquity,  many  more  ties  of  kinship  and  sympathy  than 
in  the  mighty  concave  between,  wherein  dwell  his  Christian  ancestry 
in  the  dim  light  of  scholasticism  and  theology.  —  Morison. 

The  "great  hollow"  here  so  graphically  portrayed  may  be  de- 
scribed as  the  Middle  or  Medieval  Age  (c.  450-1450  A.D.)  and  of 
these  ten  centuries  the  first  three,  or  thereabouts,  are  often  called 
the  Dark  —  as  they  certainly  were  the  darkest  —  Ages. 

The  darkest  time  in  the  Dark  Ages  was  from  the  end  of  the  sixth 
century  to  the  revival  of  learning  under  Charles  the  Great  (Charle- 
magne). Bad  grammar  was  openly  circulated  and  sometimes  com- 
mended. St.  Gregory  the  Great  quoted  the  Bible  in  depreciation  of 
the  Humanities.  (Ps.  Ixx.  15.  16.)  The  study  of  heathen  authors 
was  discouraged  more  and  more.  "Will  the  Latin  grammar  save  an 
immortal  soul  ?  "  "  What  profit  is  there  in  the  record  of  pagan  sages, 


THE  DARK  AGES  153 

the  labors  of  Hercules  or  of  Socrates  ?  "  Books  came  to  be  scarce.  .  .  . 
But  the  decline  of  education  was  not  universal.  If  studies  failed  in 
Gaul  or  Italy,  they  flourished  in  Ireland  and  afterward  in  Britain,  and 
returned  later  from  these  outer  borders  to  the  old  central  lands  of  the 
Empire.  Further,  in  spite  of  depression  and  discouragement,  there 
was  a  continuity  of  learning  even  in  the  darkest  ages  and  countries. 
Certain  school  books  hold  their  ground  .  .  .  Capella  .  .  .  Boethius  .  .  . 
Cassiodorus  .  .  .  And  later  Isodorus  of  Seville  with  a  number  of  other 
authors  are  found  in  the  ages  of  distress  and  anarchy  more  or  less 
calmly  giving  their  lectures  and  preserving  the  standards  of  a  liberal 
education.  Much  of  this  work  was  humble  enough,  but  it  was  of 
great  importance  for  the  times  that  came  after.  .  .  .  The  darkest 
ages,  with  all  then*  negligence,  kept  alive  the  life  of  the  ancient 
world. 

Boethius  [in  the  sixth  century  A.D.,  see  p.  148]  is  the  interpreter 
of  the  ancient  world  and  its  wisdom,  accepted  by  all  tlie  tribes  of 
Europe  from  one  age  to  another,  and  never  disqualified  in  his  office 
of  teacher  even  by  the  most  subtle  and  elaborate  theories  of  the  later 
schools.  .  .  .  Cassiodorus  (490-585)  is  wanting  in  the  graces  of 
Boethius,  and  he  is  much  sooner  forgotten ;  but  his  enormous  industry, 
his  organization  of  literary  production,  his  educational  zeal  have  all 
left  their  effects  indelibly  in  modern  civilization.  By  his  definition  of 
the  seven  Liberal  Arts,  and  by  his  examples  of  methods  in  teaching 
them,  he  is  the  spiritual  author  of  the  universities,  the  patron  of  all 
the  available  learning  in  the  world.  —  Ker,  Dark  Ages. 

THE  ESTABLISHMENT  OF  SCHOOLS  BY  CHARLEMAGNE.  —  We 
have  seen  above  how  the  schools  of  Athens  were  closed  by 
Justinian  in  529.  Such  schools  as  existed  after  that  time  were 
chiefly  ecclesiastical  and  their  teachings  opposed  to  pagan  or 
heathen  (i.e.  Greek)  learning.  At  length,  however,  in  787 
Charlemagne,  moved  it  is  said  by  the  troublesome  variety  of 
writing  as  well  as  the  general  illiteracy  of  his  people,  ordered  the 
establishment  of  schools  in  connection  with  every  abbey  of  his 
realm,  and  summoned  to  take  charge  of  them  Peter  of  Pisa  and 
Alcuin  of  York  (735-804)  (called  by  Guizot  "the  intellectual 
prime  minister  of  Charlemagne "),  whose  names  stand  among  the 
highest  in  a  revival  of  learning  thus  begun  in  western  Europe. 


154  A  SHORT  HISTORY  OF  SCIENCE 

In  the  later  part  of  the  eighth  century  begins  the  great  age  of 
medieval  learning,  the  educational  work  of  Charles  the  Great.  .  .  . 
There  was  some  leisure  and  freedom  and  much  literary  ambition. 
The  Latin  poets  of  the  court  of  Charlemagne  have  an  enthusiasm  and 
delight  in  classical  poetry.  ...  In  prose  there  was  no  less  activity. 
Besides  the  scientific  treatises  and  the  commentaries,  the  edifying 
works  of  Alcuin  and  others,  there  were  histories.  .  .  .  The  scholarly 
spirit  of  the  ninth  century  ...  is  not  limited  to  the  orthodox  routine. 
One  of  the  chief  scholars,  with  more  Greek  than  most  others,  Erigena, 
is  famous  for  more  than  his  learning,  as  a  philosopher,  who,  whatever 
his  respect  for  the  Church,  acknowledged  no  authority  higher  than 
reason.  —  Ker. 

Alcuin  himself  taught  rhetoric,  logic,  mathematics  and  di- 
vinity, becoming  master  of  the  great  school  at  St.  Martin's  of 
Tours.  Of  his  arithmetic  the  following  problem  is  an  illustra- 
tion :  — 

If  100  bushels  of  corn  are  distributed  among  100  people  in  such 
a  manner  that  each  man  receives  3  bushels,  each  woman  2,  and  each 
child  half  a  bushel ;  how  many  men,  women  and  children  are  there  ? 

Of  six  possible  solutions  Alcuin  gives  but  one. 

The  mathematics  taught  in  Charlemagne's  schools  would 
naturally  include  the  use  of  the  abacus,  the  multiplication  table, 
and  the  geometry  of  Boethius.  Beyond  this,  a  little  Latin  with 
reading  and  writing  sufficed  for  the  needs  of  the  church  and  her 
servants,  and  was  supplemented  by  music  and  theology  for  her 
higher  officers.  The  recognized  intellectual  needs  of  the  world 
were  indeed  but  slight.  The  civilization  of  Rome  had  been 
gradually  submerged  by  successive  waves  of  barbaric  invasion 
from  the  north,  as  a  similar  fate  was  soon  to  be  met  by  the  still 
higher  culture  of  Alexandria.  The  best  intellect  of  the  times  was 
perforce  drawn  into  other  forms  of  activity,  while  such  scholars 
as  remained  found  no  favorable  environment  for  fruitful  study. 
The  Benedictine  monasteries,  indeed,  sheltered  a  few  studious 
monks  whose  scientific  interest  scarcely  extended  beyond  the 
mathematics  necessary  for  their  simple  accounts,  and  the  com- 
putation connected  with  the  determination  of  the  date  of  Easter. 


THE  DARK  AGES  155 

Near  the  close  of  the  tenth  century  Gerbert  of  Aquitaine  (940- 
1003),  afterwards  Pope  Sylvester  II,  devoted  his  versatile  genius 
in  part  to  mathematical  science.  He  constructed  not  only  abaci, 
but  terrestrial  and  celestial  globes,  and  collected  a  valuable  library. 
To  him  were  also  attributed  a  clock,  and  an  organ  worked  by  steam. 
He  wrote  works  on  the  use  of  the  abacus,  on  the  division  of  numbers 
and  on  geometry.  The  last  named  contains  a  solution  of  the  rela- 
tively difficult  problem  to  find  the  sides  of  a  right  triangle  whose 
hypotenuse  and  area  are  given.  Unfortunately  the  latter  part  of 
his  life  was  absorbed  in  political  intrigue  and  his  death  in  1003 
cut  short  his  plans  for  attempting  the  recovery  of  the  Holy  Land. 

Out  of  the  schools  of  Charlemagne  gradually  grew  up  that 
subtle,  minute  and  over-refined  learning  of  the  later  Middle  Ages 
which  has  come  to  be  known  as  Scholasticism.  Based  as  it 
was  upon  authority  instead  of  experiment,  and  magnifying,  as  it 
did,  details  more  than  principles,  it  sharpened  rather  than  broad- 
ened the  intellect,  and  was  indifferent  if  not  unfavorable  to  science. 

REFERENCES  FOR  READING 

LUCRETIUS.    On  the  Nature  of  Things. 

STRABO.     Geography. 

PLINY.     Natural  History. 

FRONTINUS.     The  Waterworks  of  Rome.     (Tr.  by  G.  Herschel.) 

VITRUVIUS.     On  Architecture. 

KER.     The  Dark  Ages. 

GIBBON.     Decline  and  Fall  of  the  Roman  Empire. 

GALEN.     On  the  Natural  Faculties. 


CHAPTER  VIII 
HINDU  AND  'ARABIAN  SCIENCE.     THE  MOORS  IN  SPAIN 

The  grandest  achievement  of  the  Hindus  and  the  one  which, 
of  all  mathematical  investigations,  has  contributed  most  to  the 
general  progress  of  intelligence,  is  the  invention  of  the  principle  of 
position  in  writing  numbers.  —  Cajori. 

Indeed,  if  one  understands  by  algebra  the  application  of  arith- 
metical operations  to  composite  magnitudes  of  all  kinds,  whether  they 
be  rational  or  irrational  number  or  space  magnitudes,  then  the  learned 
Brahmins  of  Hindustan  are  the  true  inventors  of  algebra.  —  Hankel. 

In  the  ninth  century  the  School  of  Bagdad  began  to  flourish,  just 
when  the  Schools  of  Christendom  were  falling  into  decay  in  the  West 
and  into  decrepitude  in  the  East.  The  newly-awakened  Moslem  in- 
tellect busied  itself  at  first  chiefly  with  Mathematics  and  Medical 
Science ;  afterwards  Aristotle  threw  his  spell  upon  it,  and  an  immense 
system  of  orientalized  Aristotelianism  was  the  result.  From  the 
East,  Moslem  learning  was  carried  to  Spain ;  and  from  Spain  Aristotle 
reentered  Northern  Europe  once  more,  and  revolutionized  the  intel- 
lectual life  of  Christendom  far  more  completely  than  he  had  revolu- 
tionized the  intellectual  life  of  Islam.  —  Rashdall. 

ALEXANDRIA  fell  to  the  Arabs  in  641  A.D.  As  a  matter  of  his- 
torical perspective  it  is  noteworthy  that  the  interval  between  its 
foundation  by  Alexander  the  Great  and  its  capture  by  the 
Mohammedans,  —  during  most  of  which  period  it  was  the  in- 
tellectual centre  of  the  world,  —  is  almost  equal  to  that  between 
Charlemagne's  time  and  our  own. 

The  preservation  and  transmission  of  portions  of  Greek  science 
through  the  Dark  Ages  to  the  dawn  of  science  in  western  Europe 
about  1200  A.D.  was  mainly  effected  through  three  distinct,  though 
not  quite  independent,  channels.  First,  there  was  to  a  limited 
extent  a  direct  inheritance  of  ancient  learning  within  the  Italian 
peninsula,  through  all  its  political  and  military  turmoil.  Second, 
a  substantial  legacy  was  received  indirectly  through  the  Moors 
in  Spain ;  while,  third,  additions  of  great  importance  came  later 

156 


HINDU,   ARABIAN  AND  MOORISH  SCIENCE          157 

through  Italy  from  Constantinople.  Before  following  the  direct 
Latin-Italian  line  a  brief  sketch  of  Hindu  and  Arabic  science  is 
desirable. 

HINDU  MATHEMATICS.  —  The  far-reaching  conquests  of  Alex- 
ander the  Great  (330  B.C.)  immensely  stimulated  communica- 
tion of  ideas  between  the  Mediterranean  world  and  Asia,  and  the 
East  was  able  to  make  certain  great  contributions  to  mathematical 
science  just  where  the  Greeks  were  relatively  weakest,  namely 
in  arithmetic  and  the  rudiments  of  algebra  and  trigonometry. 
Several  centuries  before  our  era  the  Pythagorean  theorem  and  an 
excellent  approximation  for  ^2  were  known  in  India  in  connection 
with  the  rules  for  the  construction  of  altars.  The  mathematicians 
however  from  whom  we  trace  the  later  development  of  mathematics 
date  from  the  sixth  and  following  centuries. 

About  530  A.D.  Arya-bhata  wrote  a  book  in  four  parts  dealing 
with  astronomy  and  the  elements  of  spherical  trigonometry,  and 
enunciating  numerous  rules  of  arithmetic,  algebra  and  plane  trigo- 
nometry. He  gives  the  sums  of  the  series 

1    +2   +  ...  +n 

12  +  22  +  ...  +  n2 

13  +  23  +  ...  +  n*, 

solves  quadratic  equations,  gives  a  table  of  sines  of  successive  mul- 
tiples of  3f  °  —  i.e.  twenty-fourths  of  a  right  angle,  —  and  even 
uses  the  value  TT  =  3.1416,  correct  to  five  places.  His  geometry 
is  in  general  inferior. 

Some  years  later,  Brahmagupta  composed  a  system  of  as- 
tronomy in  verse,  with  two  chapters  on  mathematics.  In  this 
he  discusses  arithmetical  progression,  quadratic  equations,  areas 
of  triangles,  quadrilaterals  and  circles,  volume  and  surface  of 
pyramids  and  cones.  His  value  of  T  is  *10  =  3.16  -K  Typical 
problems  and  discussions  are  the  following :  — 

Two  apes  lived  at  the  top  of  a  cliff  of  height  100,  whose  base  was 
distant  200  from  a  neighboring  village.  One  descended  the  cliff,  and 
walked  to  the  village,  the  other  flew  up  a  height  x  and  then  flew  in  a 


158  A  SHORT  HISTORY  OF  SCIENCE 

straight  line  to  the  village.  The  distance  traversed  by  each  was  the 
same.  Find  x. 

Beautiful  and  dear  Lilavati,  whose  eyes  are  like  a  fawn's !  tell  me 
what  are  the  numbers  resulting  from  one  hundred  and  thirty-five, 
taken  into  twelve  ?  if  thou  be  skilled  in  multiplication  by  whole  or  by 
parts,  whether  by  subdivision  or  form  or  separation  of  digits.  Tell 
me,  auspicious  woman,  what  is  the  quotient  of  the  product  divided  by 
the  same  multiplier? 

The  son  of  Pritha  exasperated  in  combat,  shot  a  quiver  of  arrows 
to  slay  Carna.  With  half  his  arrows,  he  parried  those  of  his  an- 
tagonist ;  with  four  times  the  square-root  of  the  quiver-full,  he  killed 
his  horse ;  with  six  arrows,  he  slew  Salya ;  with  three  he  demolished 
the  umbrella,  standard  and  bow ;  and  with  one,  he  cut  off  the  head 
of  the  foe.  How  many  were  the  arrows,  which  Arjuna  let  fly  ? 

For  the  volume  contains  a  thousand  lines  including  precept  and 
example.  Sometimes  exemplified  to  explain  the  sense  and  bearing 
of  a  rule ;  sometimes  to  illustrate  its  scope  and  adaptation ;  one  while 
to  show  variety  of  inferences ;  another  while  to  manifest  the  principle. 
For  there  is  no  end  of  instances ;  and  therefore  a  few  only  are  exhibited. 
Since  the  wide  ocean  of  science  is  difficultly  traversed  by  men  of  little 
understanding ;  and,  on  the  other  hand,  the  intelligent  have  no  occa- 
sion for  copious  instruction.  A  particle  of  tuition  conveys  science  to  a 
comprehensive  mind ;  and  having  reached  it,  expands  of  its  own  im- 
pulse. As  oil  poured  upon  water,  as  a  secret  entrusted  to  the  vile,  as 
alms  bestowed  upon  the  worthy,  however  little,  so  does  science  infused 
into  a  wise  mind  spread  by  intrinsic  force. 

It  is  apparent  to  men  of  clear  understanding,  that  the  rule  of  three 
terms  constitutes  arithmetic;  and  sagacity,  algebra.  Accordingly  I 
have  said  in  the  chapter  of  Spherics  : 

'  The  rule  of  three  terms  is  arithmetic ;  spotless  understanding  is 
algebra.  What  is  there  unknown  to  the  intelligent  ?  Therefore,  for 
the  dull  alone,  it  is  set  forth.' 

Five  centuries  later  Bhaskara  also  wrote  an  astronomy  contain- 
ing mathematical  chapters,  and  the  contents  of  this  work  soon 
became  known  through  the  Arabs  to  western  Europe.  While  the 
preceding  writers  had  no  algebraic  symbolism,  but  depended 
laboriously  on  words  and  sentences,  Bhaskara  made  considerable 
progress  in  abbreviated  notation.  A  partial  list  of  subjects,  treated 


HINDU,  ARABIAN  AND  MOORISH  SCIENCE         159 

in  his  first  book,  includes  weights  and  measures,  decimal  numera- 
tion, fundamental  operations,  addition  etc.,  square  and  cube  root, 
fractions,  equations  of  the  first  and  second  degrees,  rule  of  three, 
progressions,  approximate  value  of  TT,  volumes.  Applications  are 
made  to  interest,  discount,  partnership,  and  the  time  of  filling 
a  cistern  by  several  fountains.  While  there  is  reason  to  believe 
that  the  decimal  system  was  known  as  early  as  the  time  of  Brahma- 
gupta,  this  work  contains  the  first  systematic  discussion  of  it, 
including  the  so-called  Arabic  numerals  and  zero. 

As  an  intermediate  stage  between  the  earlier  use  of  entire  words 
and  our  modern  employment  of  single  letters,  he  employs  abbre- 
viations, but  multiplication,  equality  and  inequality  have  still 
to  be  written  out.  The  divisor  is  written  under  the  dividend 
without  a  line,  one  member  of  an  equation  under  the  other  with 
verbal  context  to  insure  clearness.  Polynomials  are  arranged  in 
powers,  though  without  our  exponents,  coefficients  follow  the  un- 
known quantities.  In  his  "rules  of  cipher"  he  even  gives  the 
equivalent  of  a  ±  0  =  a,  O2  =  0,  V(j  =  0,  a  -h  0  =  oo. 

In  comparison  with  Greek  mathematics,  power  and  freedom 
are  gained  at  the  cost  of  some  sacrifice  of  logical  rigor.  Among 
the  Greeks,  only  the  greatest  appreciated  the  possibility  and  the 
importance  of  an  unending  series  of  numbers;  but  the  Hindu 
imagination  tended  naturally  in  this  direction.  A  notable  achieve- 
ment of  the  Hindus  was  the  introduction  of  the  idea  of  negative 
numbers  and  the  illustration  of  positive  and  negative  by  assets 
and  debts,  etc. 

On  the  whole,  the  Hindus,  having  received  a  part  of  their 
mathematics  originally  from  the  Greeks,  made  great  contributions 
on  the  arithmetical  and  algebraic  side,  their  influence  on  Euro- 
pean science  with  which  they  had  little  or  no  direct  contact  being 
exerted  mainly  through  the  Arabs. 

The  Hindu  mathematicians  had  no  interest  in  what  is  termed 
mathematical  method.  They  gave  no  definitions;  preserved  little 
logical  order;  they  did  not  care  whether  the  rules  they  used  were 
properly  established  or  not  and  were  generally  indifferent  to  funda- 
mental principles.  They  never  exalted  mathematics  as  a  subject 


160  A  SHORT  HISTORY  OF  SCIENCE 

of  study  and  indeed  their  attitude  to  learning  may  be  described  as 
decidedly  unmathematical.  —  G.  R.  Kaye. 

HINDU  ASTRONOMY.  —  In  astronomy  a  parallel  development 
took  place.  It  seems  probable  that  Greek  planetary  theory 
was  introduced  into  India  between  the  times  of  Hipparchus  and 
Ptolemy,  but  Hindu  astronomy  is  characterized  as  "a  curious 
mixture  of  old  fantastic  ideas  and  sober  geometrical  methods  of 
calculation."  Aryabhata  says  indeed  "The  sphere  of  the  stars 
is  stationary,  and  the  earth,  making  a  revolution,  produces  the 
daily  rising  and  setting  of  stars  and  planets,"  an  opinion  rejected 
by  the  later  Brahmagupta. 

MOHAMMED  AND  THE  HEGIRA.  —  During  the  sixth  and  following 
centuries  great  events  were  happening  in  Arabia,  an  anciently 
settled  country,  but  up  to  that  time  a  blank  in  the  history  of 
civilization  and  of  science.  In  569  A.D.  or  thereabouts  was  born, 
probably  in  Mecca,  —  an  insignificant  commercial  town  45  miles 
from  the  middle  eastern  shore  of  the  Red  Sea,  — that  extraordinary 
man  Mohammed,  whom  millions  of  his  fellow  men  still  regard  as 
the  Prophet  of  the  Almighty  (Allah) .  In  622  Mohammed  fled  with 
a  small  company  of  his  disciples  to  Medina,  an  agricultural  town 
250  miles  to  the  north  of  Mecca,  where  he  prosecuted  his  prop- 
aganda, and  completed  his  Koran,  —  the  Mohammedan  Bible. 
Here  also  he  died  in  632  A.D. 

In  Mecca,  Mohammed  was  "the  despised  preacher  of  a  small 
congregation,"  but  after  his  flight  (hejira)  to  Medina,  he  became 
the  leader  of  a  powerful  party  and  ultimately  the  autocratic 
ruler  of  Arabia.  Even  before  his  death  his  followers  numbered 
thousands,  while  the  religious  zeal  with  which  they  were  fired 
has  never  been  surpassed.  Taught  by  Mohammed  to  convert 
or  kill,  they  threw  themselves  upon  their  neighbors  with  a 
fanatical  fury  which  overcame  all  obstacles,  so  that  within  one 
short  century  their  religion  and  its  adherents  swept  like  a  tidal 
wave  from  the  barren  valleys  of  western  Arabia  northward  and 
eastward  through  Syria  over  Asia  Minor  and  Mesopotamia,  and 
northwestward  along  the  African  shores  of  the  Mediterranean  to 


HINDU,   ARABIAN  AND  MOORISH  SCIENCE         161 

the  straits  of  Gibraltar.  Egypt,  Alexandria,  and  Carthage  fell 
before  the  Mohammedans,  and  the  Arabian  or  Moslem  empire 
soon  rivalled  in  extent  its  great  predecessor,  the  Roman.  In  711 
Moslems  crossed  the  straits  of  Gibraltar  and  entered  Spain, 
soon  pushing  northward  into  western  France  as  far  as  Poitiers, 
where  their  great  western  and  northern  movement  was  finally 
checked  by  Charles  Martel,  in  732.  This  extraordinary  onrush, 
occurring  almost  within  a  single  century,  naturally  left  the  Moslems 
little  time  for  the  development  of  learning  or  for  the  arts  and 
sciences.  But  after  it  was  over,  the  Mohammedan  invaders 
settled  down  in  their  various  conquered  countries  and  in  some  of 
them  cultivated  the  arts  of  peace.  The  successive  Arabian  rulers 
(beginning  with  Al-Mansur,  in  754)  patronized  learning,  and  to 
this  end  collected  Greek  manuscripts,  which,  after  the  closing  of  the 
Greek  schools  by  Justinian  in  529,  had  become  scattered  abroad. 
In  particular,  certain  Nestorian  Jews  were  brought  to  Bagdad  and 
by  them  translations  into  Arabic  were  made  of  some  of  the  works 
of  Aristotle,  Euclid,  Ptolemy,  and  other  Greek  authors.  The 
learning  of  India  was  also  drawn  upon,  especially  for  the  so-called 
Arabic  numerals.  Thus  began  a  kind  of  Arabian  science,  chiefly 
imported  at  the  outset,  but  destined  within  the  next  three  centuries 
to  take  on  characteristics  of  its  own.  It  was,  however,  under  the 
Caliph  Al-Mamun  (813-833),  who  has  been  called,  as  regards 
schools  and  learning,  the  Charlemagne  of  his  people,  that  Aristotle 
was  first  translated  into  Arabic.  Al-Mamun  caused  works  on 
mathematics,  astronomy,  medicine,  and  philosophy  to  be  translated 
from  the  Greek,  and  founded  in  Bagdad  a  kind  of  academy  called 
the  "House  of  Science,"  with  a  library  and  an  observatory. 

ARABIAN  MATHEMATICAL  SCIENCE.  —  While  the  Arabs  them- 
selves were  not  in  general  much  addicted  to  scientific  pursuits, 
their  relations  to  the  Greeks  and  Hindus,  and  subsequently  to  the 
nations  of  western  Europe  are  of  very  great  importance  in  the 
history  of  science.  Even  if  we  accept  as  typical  the  traditional 
dictum  attributed  to  the  Caliph  Omar,  that  whatever  in  the  library 
of  Alexandria  agreed  with  the  Koran  was  superfluous,  whatever 
disagreed  was  worse,  and  all  should  therefore  be  destroyed,  it  was 


162 


A  SHORT  HISTORY  OF  SCIENCE 


inevitable  that  individuals  in  this  active-minded  race  should  fall 
under  the  spell  of  Greek  mathematical  science.  Their  religion 
was  in  fact  more  tolerant  towards  science  than  was  contemporary 
Christianity. 

It  would  appear  that  by  900  A.D.  the  Arabs  were  familiar  on  the 
one  hand  with  Brahmagupta's  arithmetic  and  algebra,  including 
the  decimal  system,  and  on  the  other  hand  with  the  chief  works  of 
the  great  Greek  mathematicians,  some  of  which  have  come  down 
to  us  only  through  Arabic  translations. 

The  Algebra  of  Alkarismi  written  about  830  was  based  on  the 
work  of  Brahmagupta,  and  served  in  turn  as  the  foundation  for 
many  later  treatises.  From  its  title  is  derived  our  word  "  algebra," 
from  the  author's  name  our  "  algorism."  The  book  begins :  — 

The  love  of  the  sciences  with  which  God  has  distinguished  Al- 
Mamun,  ruler  of  the  faithful,  and  his  benevolence  to  scholars,  have 
encouraged  me  to  write  a  short  work  on  computation  by  completion 
and  reduction.  Herein  I  limited  myself  to  the  simplest  matters,  and 
those  which  are  most  needed  in  problems  of  distribution,  inheritance, 
partnership,  land  measurement,  etc. 

The  first  book  contains  a  discussion  of  five  types  of  quadratic 
equations : 
ax2  =  bx,  ax2  =  c,  ax2  +  bx  =  c,  ax2  +  c  =  bx,  ax2  =  bx  +  c ; 

only  real  positive  roots  are  accepted,  but,  unlike  the  Greeks,  he 
recognizes  the  existence  of  two  roots.  He  gives  a  geometri- 

§J A  cal   solution  of    the    quadratic   equation 

analogous  to  those  of   Euclid.     Suppose 
C  x2  +  Wx  =  39    and     let    AB  =  BC  =  x, 
AH  =  CF  =  5;     then     the     areas     are 
AC  =  x2,  AK  =  BF  =  5z. 

The  sum  of  these  is  x2  +  Wx.     Com- 
plete the  square  HF  by  adding  KE  =  25. 
~G F     HF  =  (x  +  5)2  =  64,  whence  x  =  3. 
The  series  ln  +  2n  +  3n  +  ...  +  mn  was  summed  for  n  =  1,2,3,4, 
and  about  1000  A.D.  Alkayami  is  said  to  have  asserted  the  im- 
possibility of  finding  two  cubes  whose  sum  should  be  a  cube.     Even 


HINDU,  ARABIAN  AND  MOORISH  SCIENCE         163 

a  cubic  equation  was  solved  by  the  aid  of  intersecting  conic  sec- 
tions. There  is  no  definite  separation  of  algebra  and  arithmetic, 
and  the  former,  in  spite  of  relatively  rapid  development,  remains 
entirely  rhetorical.  The  division  line  of  fractions  is  introduced 
and  the  check  of  computation  by  "casting  out  nines." 

In  Physics,  Al-Hazen  (965  ?  — 1038)  wrote  a  work  on  optics 
enunciating  the  law  of  reflection  and  making  a  study  of  spherical 
and  parabolic  mirrors.  He  also  devised  an  apparatus  for  studying 
refraction,  being  probably  the  first  physicist  to  note  the  magnify- 
ing power  of  spherical  segments  of  glass  —  i.e.  lenses.  He  gave 
a  detailed  account  of  the  human  eye,  and  attempted  to  explain 
the  change  of  apparent  shape  of  the  sun  and  the  moon  when  ap- 
proaching the  horizon.  The  Arabs  employed  the  pendulum  for 
time  measurement,  and  tabulated  specific  gravities  of  metals,  etc. 
In  the  words  of  a  modern  physicist :  — 

The  Arabs  have  always  reproduced  what  came  down  to  them  from 
the  Greeks  in  thoroughly  intelligible  form,  and  applied  it  to  new  prob- 
lems, and  thus  built  up  the  theorems,  at  first  only  obtained  for  par- 
ticular cases,  into  a  greater  system,  adding  many  of  their  own.  They 
have  thus  rendered  an  extraordinarily  great  service,  such  as  would 
correspond  in  modern  times  to  the  investigations  which  have  grown 
out  of  the  pioneer  work  of  such  men  as  Newton,  Faraday  and  Rbntgen. 

—  Wiedemann. 

ARABIAN  ASTRONOMY.  —  In  connection  with  astronomy  the 
Arabs,  following  Greek  precedents,  developed  trigonometry,  in- 
troducing sines  and  other  functions  since  current.  They  used 
masonry  quadrants  of  large  size,  and  even  a  combination  of  a 
horizontal  circle  with  two  revolving  quadrants  mounted  upon  it, 
foreshadowing  the  modern  theodolite.  Better  and  more  com- 
plete observational  data  facilitated,  and  at  the  same  time  de- 
manded, improved  mathematical  methods,  while  the  necessary 
computations  were  accomplished  much  more  economically,  through 
the  use  of  the  decimal  number  system.  Haroun  Al-Raschid  sent 
to  Charlemagne  an  ingenious  water  clock,  while  under  his  suc- 
cessor, Al-Mamun,  two  learned  mathematicians  were  commis- 
sioned to  measure  a  degree  of  the  earth's  circumference. 


164  A  SHORT  HISTORY  OF  SCIENCE 

'  Choose  a  place  in  a  level  desert  and  determine  its  latitude.  Then 
draw  the  meridian  line  and  travel  along  it  towards  the  pole-star. 
Measure  the  distance  in  yards.  Then  measure  the  latitude  of  the 
second  place.  Subtract  the  latitude  of  the  first  and  divide  the  differ- 
ence into  the  distance  of  the  places  in  parasangs.  The  result  multi- 
plied by  360  gives  the  circumference  of  the  earth  in  parasangs.' 

—  Wiedemann. 

The  writer  just  quoted  describes  a  second  method  involving 
the  measurement  of  the  angle  of  depression  of  the  horizon  as 
seen  from  the  top  of  a  high  mountain. 

It  is  not  improbable  that  western  Europe  acquired  from 
eastern  Asia,  through  Arab  channels,  the  mariner's  compass  and 
gunpowder. 

*  When  the  night  is  so  dark  that  the  captains  can  perceive  no  star  to 
orient  themselves,  they  fill  a  vessel  with  water  and  place  it  in  the  in- 
terior of  the  ship,  protected  from  wind ;  then  they  take  a  needle  and 
stick  it  into  a  straw,  forming  a  cross.  They  throw  this  upon  the  water 
in  the  vessel  mentioned  and  let  it  swim  on  the  surface.  Hereupon  they 
take  a  magnet,  put  it  near  the  surface  of  the  water,  and  turn  their 
hands.  The  needle  turns  upon  the  water;  then  they  draw  their 
hands  suddenly  and  rapidly  back,  whereupon  the  needle  points  in 
two  directions,  namely  north  and  south/  1232  A.  D. 

—  Wiedemann. 

The  astronomical  theory  of  the  Arabs  was  merely  that  of 
Ptolemy.  But  they  "were  not  content  to  consider  the  Ptolemaic 
system  merely  as  a  geometrical  aid  to  computation ;  they  required 
a  real  and  physically  true  system  of  the  world,  and  had  therefore 
to  assume  solid  crystal  spheres  after  the  manner  of  Aristotle. " 
The  various  attempts  to  devise  a  better  system  all  miscarried, 
their  authors  having  no  new  guiding  principle,  nor  superior  mathe- 
matical power,  and  being  more  or  less  hampered  by  Aristotelian 
traditions,  though  Greek  theories  of  the  rotation  of  the  earth 
seem  not  to  have  been  unknown. 

ASIATIC  OBSERVATORIES.  —  Besides  the  work  of  the  Arabian 
astronomers  themselves,  it  is  an  interesting  fact  that  their  bar- 
barian Mongol  conquerors  in  the  East  acquired  a  temporarily 


HINDU,  ARABIAN  AND  MOORISH  SCIENCE          165 

active  scientific  interest,  founding  a  fine  observatory  at  Meraga 
near  the  northwest  frontier  of  modern  Persia.  The  instruments 
used  here  are  said  to  have  been  superior  to  any  used  in  Europe  until 
the  time  of  Tycho  Brahe  in  the  sixteenth  century.  The  principal 
achievement  of  this  observatory  was  the  issue  of  a  revised  set  of 
astronomical  tables  for  computing  the  motions  of  the  planets, 
together  with  a  new  star  catalogue.  The  excellence  of  their  work 
may  be  inferred  from  a  determination  of  the  precession  of  the 
equinoxes  within  1".  This  development  lasted  only  a  few  years 
in  the  latter  half  of  the  thirteenth  century.  A  similar  brief  out- 
burst of  astronomical  activity  occurred  among  the  Tartars  at 
Samarcand  (Russian  Turkestan)  nearly  200  years  later,  that  is,  a 
little  before  the  time  of  Copernicus,  and  here  the  first  new  star 
catalogue  since  that  of  Ptolemy  was  compiled.  It  is  noteworthy 
that  there  was  no  hostility  between  science  and  the  Moham- 
medan church.  One  of  the  uses  of  astronomy  indeed  was  to  de- 
termine the  direction  of  Mecca. 

No  great  original  idea  can  be  attributed  to  any  of  the  Arab  and 
other  astronomers  here  discussed.  They  had,  however,  a  remark- 
able aptitude  for  absorbing  foreign  ideas,  and  carrying  them  slightly 
further.  They  were  patient  and  accurate  observers,  and  skilful 
calculators.  We  owe  to  them  a  long  series  of  observations,  and 
the  invention  or  introduction  of  several  important  improvements 
in  mathematical  methods.  .  .  .  More  important  than  the  actual 
contributions  of  the  Arabs  to  astronomy  was  the  service  that  they 
performed  in  keeping  alive  interest  in  the  science  and  preserving  the 
discoveries  of  their  Greek  predecessors.  —  Berry. 

THE  MOORS  IN  SPAIN. — We  have  already  touched  above  upon 
the  rapid  spread  of  Mohammedanism  westward  from  its  home 
in  Arabia,  and  the  remarkable  conquests  of  its  followers  in  Spain 
and  western  France.  These  western  Mohammedans  included 
not  only  some  of  pure  Arabian  stock,  but  more  of  mixed  descent, 
especially  from  that  part  of  northern  Africa  once  known  as  Maure- 
tania,  —  whence  the  term  Moors,  generally  applied  to  the  con- 
quering Mohammedans  of  the  west.  The  Moors  entered  Spain 


166  A  SHORT  HISTORY  OF  SCIENCE 

early  in  the  eighth  century,  bringing  after  them  the  learning  of  the 
Arabs,  so  that  Hindu  and  Arabian  science,  and  to  some  extent 
Greek  science,  were  making  their  way  into  southwestern  Europe 
even  before  the  schools  of  Charlemagne  were  established  toward 
the  end  of  the  same  century  in  central  (Christian)  Europe.  In  the 
ninth  and  tenth  centuries  a  remarkable  civilization  arose  in  Spain,  — 
the  highest  that  the  Arabian  race  has  ever  reached.  The  develop- 
ments of  science  in  Mohammedan  Spain  are  more  or  less  typical 
of  what  occurred  throughout  the  whole  Arabian  empire,  and  in 
such  cities  as  Cordova,  Toledo,  and  Seville  a  type  of  civilization 
and  a  stage  of  learning  were  reached  higher  in  many  respects  than 
existed  at  the  same  tune  and  even  for  centuries  afterward  any- 
where in  Christian  Europe. 

Scarcely  had  the  Arabs  become  firmly  settled  in  Spain  when  they 
commenced  a  brilliant  career.  Adopting  what  had  now  become  the 
established  policy  of  the  Commanders  of  the  Faithful  in  Asia,  the 
Emirs  of  Cordova  distinguished  themselves  as  patrons  of  learning, 
and  set  an  example  of  refinement  strongly  contrasting  with  the  con- 
dition of  the  native  European  princes.  Cordova,  under  their  ad- 
ministration, at  its  highest  point  of  prosperity,  boasted  of  more  than 
two  hundred  thousand  houses,  and  more  than  a  million  of  inhabitants. 
After  sunset,  a  man  might  walk  in  a  straight  line  for  ten  miles  by  the 
light  of  the  public  lamps.  Seven  hundred  years  after  this  time  there 
was  not  so  much  as  one  public  lamp  in  London.  Its  streets  were 
solidly  paved.  In  Paris,  centuries  subsequently,  whoever  stepped  over 
his  threshold  on  a  rainy  day  stepped  up  to  his  ankles  in  mud. 

—  Draper. 

The  Mohammedans  made  some  additions  to  medical  science, 
and  yet  their  medicine  hardly  goes  beyond  that  of  Galen,  whom 
they  specially  revered.  In  alchemy  they  are  notable,  though 
more  by  their  attempts  than  their  achievements.  Too  often 
it  was  simply  a  search  for  "potable  gold"  or  other  "  elixirs  of 
life,"  "the  philosopher's  stone,"  and  the  like.  In  the  arts  and 
industries,  however,  the  Moors  deserve  special  mention.  Cordovan 
and  Morocco  leather  are  well  known.  Toledo  and  Damascus 
blades  (swords)  were  long  famous.  Arabian  horses  fur- 


HINDU,  ARABIAN  AND   MOORISH  SCIENCE         167 

nished  Europe  with  one  of  the  most  serviceable  strains  of  that 
useful  animal,  and  many  Arabian  words  have  been  adopted 
into  our  language,  e.g.  alcohol,  elixir,  algebra,  alembic,  zenith, 
nadir,  etc. 

"...  Under  the  caliphs,  Moslem  Spain  became  the  richest,  most 
populous,  and  most  enlightened  country  in  Europe.  The  palaces, 
the  mosques,  bridges,  aqueducts,  and  private  dwellings  reached  a 
luxury  and  beauty  of  which  a  shadow  still  remains  in  the  great  mosque 
of  Cordova.  New  industries,  particularly  silk  weaving,  flourished 
exceedingly,  13,000  looms  existing  in  Cordova  alone.  Agriculture, 
aided  by  perfect  systems  of  irrigation  for  the  first  time  in  Europe, 
was  carried  to  a  high  degree  of  perfection,  many  fruits,  trees  and 
vegetables  hitherto  unknown  being  introduced  from  the  East.  Mining 
and  metallurgy,  glass  making,  enamelling,  and  damascening  kept  whole 
populations  busy  and  prosperous.  From  Malaga,  Seville,  and  Almeria 
went  ships  to  all  parts  of  the  Mediterranean  loaded  with  the  rich 
produce  of  Spanish  Moslem  taste  and  industry,  and  of  the  natural  and 
cultivated  wealth  of  the  land.  Caravans  bore  to  farthest  India  and 
darkest  Africa  the  precious  tissues,  the  marvels  of  metal  work,  the 
enamels,  and  precious  stones  of  Spain.  All  the  luxury,  culture,  and 
beauty  that  the  Orient  could  provide  in  return,  found  its  way  to  the 
Moslem  cities  of  the  Peninsula.  The  schools  and  libraries  of  Spain  were 
famous  throughout  the  world ;  science  and  learning  were  cultivated 
and  taught  as  they  never  had  been  before.  Jew  and  Moslem,  in  the 
friendly  rivalry  of  letters,  made  their  country  illustrious  for  all  time 
by  the  productions  of  their  study.  .  .  .  The  schools  of  Cordova, 
Toledo,  Seville,  and  Saragossa  attained  a  celebrity  which  subsequently 
attracted  to  them  students  from  all  parts  of  the  world.  At  first  the 
principal  subjects  of  study  were  literary,  such  as  rhetoric,  poetry, 
history,  philosophy,  and  the  like,  for  the  fatalism  of  the  faith  of  Islam 
to  some  extent  retarded  the  adoption  of  scientific  studies.  To  these, 
however,  the  Spanish  Jews  opened  the  way,  and  when  the  barriers  were 
broken  down,  the  Arabs  themselves  entered  with  avidity  into  the 
domain  of  science.  Cordova  then  became  the  centre  of  scientific 
investigation.  Medicine  and  surgery  especially  were  pursued  with 
intense  diligence  and  success,  and  veterinary  surgery  may  be  said  to 
have  there  first  crystallized  into  a  science.  Botany  and  pharmacy 
also  had  their  famous  professors,  and  astronomy  was  studied  and 


168  A  SHORT  HISTORY  OF  SCIENCE 

taught  as  it  had  never  been  before;  algebra  and  arithmetic  were 
applied  to  practical  uses,  the  mariner's  compass  was  invented,  and 
science  as  applied  to  the  arts  and  manufactures  made  the  products  of 
Moslem  Spain  —  the  fine  leather,  the  arms,  the  fabrics,  and  the  metal 
work  —  esteemed  throughout  the  world.  .  .  .  Canals  and  water 
wheels  for  irrigation  carried  marvellous  fertility  throughout  the  south 
of  Spain,  where  the  one  thing  previously  wanting  to  make  the  land  a 
paradise  was  water.  Rice,  sugar,  cotton,  and  the  silkworm  were  all 
introduced  and  cultivated  with  prodigious  success ;  the  silks,  brocades, 
velvets,  and  pottery  of  Valencia,  the  beautiful  damascened  steel  of 
Seville,  Toledo,  Murcia,  and  Granada,  the  stamped  embossed  leather 
of  Cordova,  and  the  fine  cloths  of  Seville  brought  prosperity  to 
Moslem  and  Mozarab  alike  under  the  rule  of  the  Omeyyad  caliphs, 
while  the  systematic  working  of  the  silver  mines  of  Jaen,  the  corals  on 
the  Andalusian  coasts,  and  the  pearls  of  Catalonia  supplied  the  ma- 
terial for  the  lavish  splendor  which  the  rich  Arabs  affected  in  their 
attire  and  adornment. 

The  Moors  of  Andalusia  and  Valencia  acclimatized  and  cultivated 
a  large  number  of  semitropical  fruits  and  plants  hitherto  little  known 
in  Europe,  and  studied  arboriculture  and  horticulture  not  only  practi- 
cally but  scientifically.  The  famous  work  on  the  subject  by  Abu 
Zacaria  Al-Awan  was  the  foundation  of  such  books,  and  of  the  applica- 
tion of  science  to  gardening.  It  was  mainly  derived  from  Chaldean, 
Greek,  and  Carthaginian  manuscripts  now  lost.  Curiously,  Spain  had 
produced  under  the  Romans  a  famous  book  on  agriculture  by  Colu- 
mella:  but  for  scientific  knowledge  it  cannot  be  compared  to  the 
Treatise  on  Agriculture  by  Abu  Zacaria.  ,  .  .  From  the  earliest 
times  the  wool  of  Spain  had  been  the  finest  in  the  world.  .  .  .  Vast 
herds  of  stunted,  ill-looking,  but  splendidly  fleeced  sheep  belonged  to 
the  nobles  and  ecclesiastical  lords,  and  quite  early  in  the  period  of  re- 
conquest,  when  these  classes  were  all-powerful,  a  confederacy  of  sheep 
owners  was  formed,  which  by  the  fourteenth  and  fifteenth  centuries 
had  developed  into  a  corporation  of  immense  wealth.  This  was  called 
the  Mesta.  .  .  .  The  fleeces  were  extremely  fine,  often  weighing 
12  pounds  per  animal,  and  the  wool  was  sought  after  throughout  the 
world,  especially  by  Flemish  and  French  cloth  workers.  Even  in  the 
ninth  century  Spanish  wool  was  famous  in  Persia  and  in  the  East; 
and  as  early  as  the  time  of  the  Phoenicians  it  was  considered  the 
finest  in  the  world.  —  Hume. 


HINDU,  ARABIAN  AND  MOORISH  SCIENCE         169 

The  tenth  century  was  the  golden  age  of  Moorish  science  in 
Spain.  Another  hundred  years  and  it  had  gone  down  forever. 
Its  permanent  importance,  even  in  conserving  the  work  of  the 
ancients,  has  been  questioned,  and  a  recent  writer  cleverly  com- 
pares the  whole  western  movement  of  the  Arabians  to  the  sands 
of  their  deserts,  —  now  fierce  and  pitiless  when  driven  by  some 
force  such  as  the  wind,  —  now  sinking  into  inert,  helpless,  infertile 
heaps  when  left  to  themselves. 

An  Arab  renaissance  as  early  as  the  eighth  century  had  revived 
something  of  classic  knowledge.  The  poetry  and  philosophy  of  Greece 
were  studied,  and  the  taste  for  learning  was  cultivated  with  the  en- 
thusiasm which  the  Arabs  infused  into  all  their  undertakings.  Every 
one  knows  the  fascinating  account  of  these  things  in  the  pages  of 
Gibbon.  How  the  tide  of  progress  flowed  from  Samarcand  and  Bo- 
khara to  Fez  and  Cordova.  How  a  vizir  consecrated  200,000  pieces  of 
gold  to  the  foundation  of  a  college.  How  the  transport  of  a  doctor's 
books  required  four  hundred  camels.  How  a  single  library  in  Spain 
contained  600,000  volumes,  while  seventy  public  libraries  were  opened 
in  Andalusia  alone.  How  the  Arabian  schools  of  Spain  and  Italy 
were  resorted  to  by  scholars  from  every  country  in  Europe.  .  .  . 

Here  was  a  state  of  luxury  and  learning  which  contrasted  strongly 
enough  with  the  barbarism  of  the  age.  But  under  all  this  show  where 
was  the  substantial  basis?  How  much  of  all  this  was  real?  Arab 
architecture,  in  so  far  as  it  was  Arab,  and  not  built  for  them  by  the 
Greeks,  was  a  concoction  of  whim  and  fantasy.  In  those  nervous 
hands  every  strong  and  simple  feature  was  distorted  into  endless  com- 
plications, and,  as  always  happens,  lost  in  stability  what  it  gained 
in  eccentricity.  Their  learning  was  of  the  same  character.  Though 
they  disputed  interminably  on  the  rival  merits  of  the  Greek  philos- 
ophers, they  were  content  to  receive  all  their  knowledge  of  them 
through  indifferent  translations.  When  the  real  revival  of  learning 
came,  and  a  genuine  Renaissance  set  in,  the  six  or  seven  centuries  of 
Arab  civilization  were  simply  ignored  and  passed  over.  .  .  . 

The  Arab  mind  seems  to  turn  by  a  sort  of  instinct  to  the  occult, 
the  mystical,  the  fantastic.  It  is  always  sighing  for  new  worlds  to 
conquer  before  it  has  made  good  the  ground  it  stands  on.  It  has  the 
curious  gift  of  turning  everything  it  touches  from  substance  to  shadow. 


170  A  SHORT  HISTORY  OF  SCIENCE 

Astronomy  changes  into  astrology,  and  the  main  business  of  the  science 
becomes  the  casting  of  horoscopes.  The  study  of  medicine  changes 
into  the  composition  of  philtres  and  talismans  and  the  reciting  of  incan- 
tations. Chemistry  changes  into  a  search  for  the  secret  of  the  trans- 
mutation of  metals  and  the  elixir  of  immortal  health.  In  short,  the 
tendency  always  was  to  shift  the  appeal  from  the  intellect  and  reason 
to  the  fancy  and  imagination ;  and  their  zeal,  instead  of  being  devoted 
to  laying  firm  foundations,  evaporated  in  vague  aspirations  after  the 
unintelligible  or  the  unobtainable.  .  .  . 

And  the  consequence  is  that  not  only  has  the  Arab  left  us  little 
or  nothing,  but  his  whole  history  seems  already  more  legendary  than 
real.  Other  civilizations  abide  our  question.  Not  the  Greek  and 
Roman  only,  but  the  remote  Assyrian  and  Egyptian,  are  definite  and 
real  in  comparison  with  the  Arabian.  This  seems  of  another  texture. 
It  is  such  stuff  as  dreams  are  made  of. 

Those  so-called  conquests  of  his  [the  Arab's]  were  really  the  taking 
advantage  of  a  unique  opportunity  for  destroying  and  pulling  down. 
The  collapse  of  the  Western  Empire,  and  weakness  and  paralysis  of 
the  Eastern,  afforded  the  Arab  a  fine  field  for  the  display  of  his  peculiar 
prowess.  He  took  to  the  lumber  and  debris  of  these  crumbling  empires 
as  fire  takes  to  rotten  wood.  But  if  in  the  void  that  separates  ancient 
civilisation  from  modern  the  Arab  appears  to  advantage,  there  no 
sooner  entered  on  the  scene  nations  of  solid  character  and  creative 
genius  than  he  retired  before  them,  and  yielded  to  their  advance. 

—  March  Phillips. 

The  Golden  Age  of  Moorish  learning  in  the  tenth  century  came 
and  went,  leaving  behind  it  singularly  few  permanent  results. 
Owing  to  the  racial  and  religious  hatreds  of  the  time  the  Christian 
conquerors  of  the  Moslems,  like  their  Roman  prototypes  in  the 
first  few  centuries  after  Christ,  had  small  respect  for  Greek  —  and 
less  for  Mohammedan  —  learning.  Hence,  doubtless,  it  came 
about  that  to-day  in  Cordova,  for  example,  almost  no  traces  re- 
main of  that  Arabian  learning  of  which  it  was  once  the  celebrated 
seat.  Even  the  site  of  its  illustrious  university  has  faded  from 
memory  and  only  its  great  mosque  (of  which  the  heart  is  occupied 
by  a  Christian  church)  remains  to  bear  visible  witness  to  Moham- 
medan Cordova.  The  same  is  true  of  other  once  famous  centres 


HINDU,   ARABIAN  AND   MOORISH  SCIENCE         171 

of  Spanish  Mohammedan-Greek  learning.  Toledo  still  possesses 
some  of  its  Arabian  walls  and  gateways,  and  Seville  its  lovely 
Giralda  —  "  the  first  astronomical  observatory  in  Europe  "  —  and 
its  Tower  of  Gold ;  but  it  is  only  in  the  Alhambra  of  Granada 
that  any  adequate  vision  can  be  had  of  Mohammedan  life  and 
influence  in  Spain.  Here  the  quiet,  the  seclusion,  the  rich  orna- 
mentation, and  the  music  of  abundant  running  waters,  still  com- 
municate an  impression  of  wealth,  taste,  and  power,  and  suggest 
possibilities  of  uninterrupted  study  and  an  intellectual  life.  Else- 
where, evidences  of  the  Mohammedan  love  of  inquiry,  of  libraries, 
of  decoration,  and  even  of  fruits  and  gardens,  have  been  almost 
wholly  blotted  out. 

REFERENCES  FOR  READING 

BALL.    Chapter  IX. 

BERRY.     Chapter  III. 

DRAPER.     History  of  the  Intellectual  Development  of  Europe.     Vol.  II. 

DREYER.     Chapter  XI. 

HUME,  M.     History  of  the  Spanish  People. 

MARCH  PHILLIPS.    In  the  Desert. 

GIBBON.    Decline  and  Fall. 


CHAPTER  IX 
PROGRESS  OF  SCIENCE  TO  1450  A.D. 

It  cannot  be  too  emphatically  stated  that  there  is  no  historical 
evidence  for  the  theory  which  connects  the  new  birth  of  Europe  with 
the  passing  away  of  the  fateful  millennial  year  and  with  it,  the  awful 
dread  of  a  coming  end  of  all  things.  Yet,  although  there  was  no  breach 
of  historical  continuity  at  the  year  1000,  the  date  will  serve  as  well  as 
any  other  that  could  be  assigned  to  represent  the  turning-point  of 
European  history,  separating  an  age  of  religious  terror  and  theological 
pessimism  from  an  age  of  hope  and  vigor  and  active  religious  en- 
thusiasm. .  .  .  The  change  which  began  to  pass  over  the  schools  of 
France  in  the  eleventh  century  and  culminated  in  the  great  intellectual 
Renaissance  of  the  following  age,  was  but  one  effect  of  that  general 
revivification  of  the  human  spirit  which  should  be  recognized  as  con- 
stituting an  epoch  in  the  history  of  European  civilization  not  less 
momentous  than  the  Reformation  or  the  French  Revolution.  .  .  . 
The  schools  of  Christendom  became  thronged  as  they  were  never 
thronged  before.  A  passion  for  inquiry  took  the  place  of  the  old 
routine.  The  Crusades  brought  different  parts  of  Europe  into  con- 
tact with  one  another  and  into  contact  with  the  new  world  of  the  East, 
—  with  a  new  Religion  and  a  new  Philosophy,  with  the  Arabic  Aris- 
totle, with  the  Arabic  commentators  on  Aristotle,  and  eventually  even 
with  Aristotle  in  the  original  Greek.  .  .  .  Whatever  the  causes  of 
the  change,  the  beginning  of  the  eleventh  century  represents,  as  nearly 
as  it  is  possible  to  fix  it,  the  turning-point  in  the  intellectual  history  of 
Europe.  —  Rashdall. 

THE  CRUSADES.  —  From  the  time  of  Mohammed's  hegira 
from  Mecca  to  Medina  in  622  A.D.  to  the  siege  of  Vienna  by  his 
followers  in  1683  —  a  period  of  more  than  1000  years  —  Europe 
stood  in  constant  dread  of  Mohammedan  conquest.  Fifteen  years 
after  the  hegira,  Jerusalem  was  captured  by  Omar,  and  remained 
under  Mohammedan  control  till  the  end  of  the  first  Crusade,  since 
which  time  it  has  been  sometimes  in  Christian,  sometimes  in 
Mohammedan,  possession.  Toleration  of  Christians  in  the  Holy 

172 


PROGRESS  OF  SCIENCE  TO   1450  A.D.  173 

Land  was,  however,  the  rule  until  the  eleventh  century,  and 
between  700  and  1000  A.D.  pilgrimages  to  Jerusalem  were  fre- 
quently undertaken  by  Christians  in  the  West.  But  after  1010 
such  pilgrimages  began  to  be  seriously  interfered  with,  and  matters 
steadily  grew  worse,  until  in  1071  Seljukian  Turks  displaced 
Arabian  Mohammedans  as  rulers  of  Jerusalem.  These  Turks, 
though  more  rough  than  intolerant,  eventually  interfered  with  both 
trade  and  pilgrimages,  until  for  this  and  other  reasons  the  conquest 
of  the  Holy  Land  became  a  passion  with  the  Christian  nations. 

In  the  spring  of  1097,  after  several  years  of  widespread  prepara- 
tion, a  great  host  of  western  Christians,  variously  estimated  at 
150,000  to  600,000,  gathered  at  Constantinople  charged  with  war- 
like and  religious  zeal  and  bent  on  wresting  Jerusalem  and  the 
Holy  Land  from  the  possession  of  the  Mohammedan  "  Infidel." 
This  was  the  beginning  of  those  expeditions  under  the  banner  of 
the  Cross,  —  hence  known  as  the  Crusades,  —  which  may  be 
regarded  as  intermittent  reactions  of  the  Christian  West  against 
the  pressure  of  the  Mohammedan  East.  The  spirit  of  Christian 
Europe  in  the  Middle  Ages  being  essentially  religious  and  ec- 
clesiastical, it  was  natural  that  its  more  bold  and  adventurous 
youth  should  regard  with  jealousy  and  indignation  the  wide 
extent  of  the  Mohammedan  empire  and  especially  its  possession 
of  Jerusalem  and  other  holy  places.  In  all,  eight  such  Crusades 
are  recognized  by  historians,  and  of  these  the  influence  upon 
Christian  Europe  must  have  been  immense.  In  the  first  place, 
the  expansion  of  the  intellectual  outlook  due  to  the  mere  experiences 
of  travel,  for  men  born  and  bred  under  the  parochial  limitations 
of  feudalism  and  monasticism,  must  have  been  great.  Then,  too, 
the  arts  and  appliances  observed  abroad,  the  different  stand- 
ards of  all  sorts,  the  wealth  and  luxury  of  the  distant  East,  doubt- 
less had  a  powerful  effect  upon  Europe  when  reported  or  intro- 
duced by  the  Crusaders  upon  their  return.  When  we  reflect  upon 
the  ages  of  darkness  which  had  rested  upon  Christian  Europe  from 
the  fall  of  Rome  into  the  hands  of  the  barbarians  to  the  fall  of 
Jerusalem  into  the  hands  of  the  Turks  —  a  period  of  almost 
exactly  six  hundred  years  —  we  may  agree  with  those  who  are 


174  A  SHORT  HISTORY  OF  SCIENCE 

disposed  to  look  upon  the  Crusades  as  an  age  of  discovery  com- 
parable with  that  of  the  new  world  by  Columbus  and  his  follow- 
ers, —  but  a  discovery  of  the  East  instead  of  the  West. 

The  period  of  the  Crusades  extends  over  about  two  centuries, 
viz :  —  from  1090  to  1290,  and  thus  immediately  precedes  the 
Renaissance,  of  which  it  was  apparently  one  of  the  most  im- 
portant factors. 

TRIVIUM:  QUADRIVIUM.  SCHOLASTICISM.  —  Meantime,  follow- 
ing the  mandate  of  Charlemagne  establishing  schools  in  connection 
with  all  the  abbeys  and  monasteries  of  his  vast  domain  of  central 
Europe,  a  characteristic  technical  and  essentially  verbal  scholarship 
gradually  arose  which,  although  chiefly  ecclesiastical  in  substance, 
and  so  narrow  in  its  range  as  almost  completely  to  neglect  natural 
science,  was  often  thorough  and  sometimes  profound.  This 
learning  in  its  later  development  is  known  as  "Scholasticism,"  of 
which  the  foundation  and  essence  was  the  famous  curriculum  of 
"the  seven  liberal  arts,"  founded  upon  the  educational  doctrines 
of  Plato,  but  adapted  to  the  fashion  of  the  Middle  Ages.  These 
consisted  of  a  quadriwum  —  geometry,  astronomy,  music  and  arith- 
metic—  and  a  trivium  —  grammar,  logic,  and  rhetoric,  (p.  148.) 

In  the  introduction  to  the  Logic  of  Aristotle  which  was  in  the 
hands  of  every  student  even  in  the  Dark  Ages,  the  Isagoge  of  Por- 
phyry, the  question  was  explicitly  raised  in  a  very  distinct  and 
emphatic  manner.  The  words  in  which  this  writer  states,  without 
resolving,  the  problem  of  the  Scholastic  Philosophy,  have  played  per- 
haps a  more  momentous  part  in  the  history  of  thought,  than  any 
other  passage  of  equal  length  in  all  literature  outside  the  canonical 
Scriptures.  They  are  worth  quoting  at  length : 

'  Next,  concerning  genera  and  species,  the  question  indeed  whether 
they  have  a  substantial  existence,  or  whether  they  consist  in  bare 
intellectual  concepts  only,  or  whether,  if  they  have  a  substantial  ex- 
istence, they  are  corporeal  or  incorporeal,  and  whether  they  are  sep- 
arable from  the  sensible  properties  of  the  things  (or  particulars  of 
sense),  or  are  only  in  those  properties  and  subsisting  about  them,  I 
shall  forbear  to  determine.  For  a  question  of  this  kind  is  a  very  deep 
one  and  one  that  requires  a  longer  investigation/  —  Rashdall. 


PROGRESS   OF  SCIENCE  TO   1450  A.D.  175 

To  show  the  low  state  of  natural  history  it  suffices  to  refer  to 
an  extraordinary  work,  the  so-called  Physiologus  or  Bestiary,  a 
kind  of  scriptural  allegory  of  animal  life,  originally  Alexandrian, 
but  surviving  in  mutilated  forms  and  widely  used  in  medieval 
times.  The  childish  and  grotesque  character  of  this  curious 
compendium  shows  how  ill-adapted  were  the  centuries  of  crusad- 
ing to  the  calm  pursuits  of  science ;  they  were  indeed  almost  barren 
in  this  direction. 

Scholasticism,  nevertheless,  lingered  long  after  the  Crusades 
were  ended,  and  abundant  survivals  of  it  exist  even  today. 

MEDIEVAL  UNIVERSITIES.  —  The  origin  of  the  universities  which 
play  so  great  a  part  in  the  cultivation  and  dissemination  of  learn- 
ing in  the  later  middle  ages  is  involved  in  obscurity.  The  medical 
school  at  Salerno  in  southern  Italy  seems  to  have  become  known 
in  the  ninth  century,  so  that  the  University  of  Salerno  is  some- 
times called  the  oldest  in  Europe.  It  was  still  famous  in  the 
thirteenth  century.  The  law  school  at  Bologna,  in  northern 
Italy,  became  well  known  about  1000  A.D.,  though  the  date  of 
the  University  of  Bologna  is  usually  given  as  near  the  end  of  the 
twelfth  century.  The  University  of  Paris  is  often  dated  from 
the  early  part  of  the  same  century.  None  of  these  early  univer- 
sities was  much  more  than  an  association  or  gild  of  masters  and 
pupils.  Laboratories  for  instruction  were  of  course  unknown. 

In  the  eleventh  and  twelfth  centuries  there  was  a  gradual  de- 
velopment from  the  previous  monastic  schools  to  the  beginnings 
of  modern  universities  at  Paris,  Bologna,  Salerno,  Oxford,  and 
Cambridge,  the  schools  themselves  however  continuing  along 
their  previous  lines ;  and  from  that  time  onward  to  our  own,  the 
universities  have  played  the  chief  part  in  the  advancement  of 
learning  in  general  and  of  science  in  particular.  In  their  develop- 
ment theological  influences  were  naturally  dominant,  and  it  is 
interesting  to  observe  that  the  use  of  Aristotle's  Natural  Philoso- 
phy, which  became  later  the  stronghold  of  orthodox  conserva- 
tism, was  prohibited  in  the  thirteenth  century. 

Medieval  academic  standards  were  naturally  low.  The  univer- 
sity was  a  voluntary  and  privileged  society  of  scholars.  Not  until 


176  A  SHORT  HISTORY  OF  SCIENCE 

1426  is  there  a  record  of  the  refusal  of  a  degree  for  poor  scholarship, 
and  the  victim  then  sought  redress  by  legal  proceedings,  though 
in  vain.  In  most  of  the  early  universities  logic,  philosophy,  and 
theology  were  cultivated  rather  than  even  mathematical  science. 

TRANSMISSION  OF  SCIENCE  THROUGH  MOORISH  SPAIN.  —  The 
meagre  rivulet  of  classical  science  derived  directly  from  Greek 
and  Roman  sources  is  now  mingled  with  the  current  which  found 
its  way  through  northern  Africa  and  Spain  under  the  Moors. 
Boethius'  rudimentary  work  was  supplanted,  and  before  1400, 
the  first  five  books  of  Euclid  were  taught  at  many  universities. 
Ptolemy's  Almagest  was  also  translated  from  the  Arabic  into 
Latin  early  in  the  twelfth  century,  probably  with  the  use  of 
Arabic  numerals.  Near  the  close  of  the  Moorish  domination  of 
Spain,  King  Alfonso  X  of  Castile  (1223-1284)  collected  at  Toledo 
a  body  of  Christian  and  Jewish  scholars  who  under  his  direc- 
tion prepared  the  celebrated  Alfonsine  Tables,  using  the  new 
Arabic  numerals.  These  enjoyed  a  high  reputation  for  three 
centuries,  though  first  printed  in  1483. 

While  we  thus  owe  to  the  Arabs  a  considerable  debt  for  pre- 
serving for  the  use  of  later  ages  the  precious  heritage  of  Greek 
learning,  the  revival  of  learning  in  the  fourteenth  century  came 
chiefly  from  other  quarters  and  would  probably  have  come  in  due 
tune  even  if  Arabic  influences  had  not  been  at  work.  Yet  it  is 
noteworthy  that  early  in  the  twelfth  century  re-translations  of  the 
Greek  classics  began  to  be  made  from  the  Arabic,  and  these  may 
well  have  supplied  the  very  limited  demand  for  them  tolerated  by 
the  church  for  the  next  hundred  years.  In  spite  of  jealous  ex- 
clusiveness  the  learning  of  the  great  schools  of  Granada,  Cordova, 
and  Seville  gradually  found  its  way  to  Paris,  Oxford,  and  Cam- 
bridge. 

During  the  course  of  the  twelfth  century  a  struggle  had  been  going 
on  in  the  bosom  of  Islam  between  the  Philosophers  and  the  Theo- 
logians. It  was  just  at  the  moment  when,  through  the  favor  of  the 
Caliph  Al-Mansur,  the  Theologians  had  succeeded  in  crushing  the 
Philosophers,  that  the  torch  of  Aristotelian  thought  was  handed  on  to 
Christendom.  , 


PROGRESS  OF  SCIENCE  TO   1450  A.D.  177 

It  was  from  this  time  and  from  this  time  only  (though  the  change 
had  been  prepared  in  the  region  of  pure  Theology  by  Peter  the  Lom- 
bard) that  the  Scholastic  Philosophy  became  distinguished  by  that 
servile  deference  to  authority  with  which  it  has  been  in  modern  times 
too  indiscriminately  reproached.  And  the  discovery  of  the  new  Aris- 
totle was  by  itself  calculated  to  check  the  originality  and  speculative 
freedom  which,  in  the  paucity  of  books,  had  characterized  the  active 
minds  of  the  twelfth  century.  The  tendency  of  the  sceptics  was  to 
transfer  to  Aristotle  or  Averroes  the  authority  which  the  orthodox 
had  attributed  to  the  Bible  and  the  Fathers  of  the  Church. 

—  Rashdall. 

DAWN  OF  THE  RENAISSANCE.  —  In  the  thirteenth  century 
it  becomes  plain  that  a  new  spirit  is  arising  in  Europe.  We 
cannot  fail  to  detect  at  this  time  the  existence,  even  at  places  as 
far  apart  as  Oxford  and  Bologna  —  infinitely  further  apart  then 
than  now,  —  of  a  widespread  desire  for  knowledge  and  a  zeal 
for  learning  such  as  had  not  been  known  for  centuries.  Arabic 
mathematical  science  is  introduced  from  northern  Africa  by 
Leonardo  Pisano.  A  fresh  and  notable  philosopher  —  Albertus 
Magnus  —  appears.  Thomas  Aquinas  writes  his  famous  Imi- 
tatio  Christi.  Great  Gothic  cathedrals  arise,  more  universities  are 
founded,  and,  most  noteworthy  of  all  for  the  history  of  science, 
an  original  student  of  nature  appears,  in  Roger  Bacon. 

By  the  beginning  of  the  thirteenth  century,  in  consequence  of 
the  opening  up  of  communications  with  the  East  —  through  inter- 
course with  the  Moors  in  Spain,  through  the  conquest  of  Constanti- 
nople, through  the  Crusades,  through  the  travels  of  enterprising  scholars 
—  the  whole  of  the  works  of  Aristotle  were  gradually  making  their 
way  into  the  Western  world.  Some  became  known  in  translations 
direct  from  the  Greek;  more  in  Latin  versions  of  older  Syriac  or 
Arabic  translations.  And  now  the  authority  which  Aristotle  had 
long  enjoyed  as  a  logician  —  nay,  it  may  almost  be  said  the  authority 
of  logic  itself  —  communicated  itself  in  a  manner  to  all  that  he  wrote. 
Aristotle  was  accepted  as  a  well-nigh  final  authority  upon  Meta- 
physics, upon  Moral  Philosophy,  and  with  far  more  disastrous  results 
upon  Natural  Science.  The  awakened  intellect  of  Europe  busied 


178  A  SHORT  HISTORY  OF  SCIENCE 

itself  with  expounding,  analysing  and  debating  the  new  treasures 
unfolded  before  its  eyes.  .  .  . 

And  of  the  scientific  side  of  this  revival  Italy  was  the  centre. 
This  branch  of  the  movement  began,  indeed,  before  the  twelfth 
century.  It  was  in  Italy  that  the  Latin  world  first  came  into  con- 
tact with  the  half-forgotten  treasures  of  Greek  wisdom,  with  the 
wisdom  which  the  Arabs  had  borrowed  from  the  Greeks  and  with 
original  products  of  the  remoter  East.  Of  the  Medical  School  of  Sa- 
lerno we  have  already  spoken.  It  was  probably  in  Italy  and  through 
the  Arabic  that  the  Englishman  Adelard  of  Bath  translated  Euclid 
into  Latin  during  the  first  half  of  the  eleventh  century.  At  about 
the  same  time  modern  musical  notation  originated  with  the  discoveries 
of  the  Camaldulensian  monk,  Guido  of  Arezzo.  In  the  first  years  of 
the  following  century  the  Algebra  and  the  Arithmetic  which  the 
Arabs  had  borrowed  from  the  Hindus  were  introduced  into  Italy 
by  the  Pisan  merchant,  Leonardo  Fibonacci.  .  '.'."*  It  was  to  this 
Arabo-Greek  influence  that  Bologna  owed  its  very  important  School 
of  Medicine  and  Mathematics — two  subjects  more  closely  connected 
then  than  now  through  their  common  relationship  to  Astrology. 

-Rashdall 

MATHEMATICAL  SCIENCE  IN  THE  THIRTEENTH  CENTURY.  — 
Increasing  activity  in  mathematical  science  was  due  largely  to 
Leonardo  Pisano  of  Italy,  Jordanus  Nemorarius  of  Saxony,  and 
Roger  Bacon  of  England. 

Leonardo  Pisano  or  Fibonacci  (born  1175)  was  educated  in 
Barbary,  where  his  father  was  in  charge  of  the  custom-house,  and 
thus  became  familiar  with  Alkarismi's  algebra,  and  the  Arabic 
decimal  system.  He  appreciated  their  advantages  and  on  his 
return  to  Italy  published  in  his  Liber  Abaci  an  account  which 
gave  them  currency  in  Europe  "in  order  that  the  Latin  race 
might  no  longer  be  deficient  in  that  knowledge."  As  the  mathe- 
matical masterpiece  of  the  Middle  Ages,  it  remained  a  standard 
for  more  than  two  centuries.  His  algebra  is  rhetorical,  but  gains 
by  the  employment  of  geometrical  methods.  He  discusses  the 
fundamental  operations  with  whole  numbers  and  fractions,  using 
the  present  line  for  division.  Fractions  are  decomposed  into  parts 
with  unit  numerators  as  in  early  Egypt.  Through  the  Arabs 


PROGRESS  OF  SCIENCE  TO  1450  A.D.  179 

Leonardo  inherits  Egyptian  as  well  as  Greek  traditions,  for  ex- 
ample, the  type  of  fraction  just  mentioned,  square  and  cube  root, 
progressions,  the  method  of  false  assumption.  It  would  appear 
that  when  the  Arabs  conquered  Alexandria  some  of  the  old 
Egyptian  culture  was  preserved.  The  rule  of  three,  partner- 
ship, powers  and  roots,  and  the  solution  of  equations  are  also 
included. 

In  1225  the  emperor,  impressed  by  the  accounts  of  Pisano's 
mathematical  power,  arranged  a  mathematical  tournament  of 
which  the  challenge  questions  are  preserved : 

'  To  find  a  number  of  which  the  square,  when  either  increased  or 
diminished  by  5,  would  remain  a  square. 

'To  find  by  the  methods  used  in  the  tenth  book  of  Euclid  a  line 
whose  length  x  should  satisfy  the  equation  x3  -f-  2x2  +  Wx  =  20. 

'  Three  men,  A,  B,  C,  possess  a  sum  of  money  u,  their  shares  being 
in  the  ratio  3:2:1.  A  takes  away  x,  keeps  half  of  it,  and  deposits 
the  remainder  with  D ;  B  takes  away  y,  keeps  f  of  it,  and  deposits 
the  remainder  with  D ;  C  takes  away  all  that  is  left,  namely  z,  keeps 
f  of  it,  and  deposits  the  remainder  with  D.  This  deposit  is  found 
to  belong  to  A,  B,  and  C  in  equal  proportions.  Find  u,  x,  y  and  z.' 
Leonardo  gave  a  correct  solution  of  the  first  and  third,  also  a  root 
of  the  cubic  equation  correct  to  nine  decimals.  —  Ball. 

Jordanus  Nemorarius  wrote  important  Latin  works  on  arith- 
metic, geometry,  and  astronomy.  His  De  Triangulis  —  the  most 
important  of  these  —  consists  of  four  books  dealing  not  only 
with  triangles,  but  with  polygons  and  circles.  He  generally  uses 
Arabic  numerals,  and  denotes  quantities  known  or  unknown  by 
letters.  He  solves  the  problem  of  finding  two  numbers  having  a 
given  sum  and  product,  by  a  method  equivalent  to  our  elemen- 
tary algebra.  This  is  practically  the  first  European  syncopated 
algebra,  but  seems  to  have  become  too  little  known  to  have  far- 
reaching  results  in  a  time  not  yet  ripe  for  this  invention.  A  book 
on  Weights  contains  elements  of  mechanics. 

Albertus  Magnus,  born  near  the  end  of  the  twelfth  century, 
became  an  ardent  champion  of  the  newly  discovered  but  pro- 
scribed works  of  Aristotle.  In  particular  he  interpreted  the  Milky 


180  A  SHORT  HISTORY  OF  SCIENCE 

Way  as  an  accumulation  of  small  stars,  and  ridiculed  the  current 
objections  to  antipodes,  striving,  however,  always  to  harmonize 
the  ancient  science  with  the  theology  of  his  church. 

Two  Oxford  scholars,  John  of  Holywood  (Sacrobosco)  and  Roger 
Bacon,  have  next  to  be  mentioned.  Sacrobosco  lectured  at  Paris 
on  arithmetic  and  algebra,  and  wrote  standard  books  on  the  former 
with  rules  but  no  proofs,  and  an  astronomy  of  which  more  than 
sixty  editions  were  afterwards  printed. 

ROGER  BACON  (1214-1294?).  —  In  the  history  of  natural  science 
one  thirteenth  century  name  stands  out  before  all  others,  viz. : 
that  of  Roger  or  "Friar"  Bacon,  a  member  of  the  Franciscan 
order,  born  at  Ilchester,  England,  in  1214.  He  was  a  pupil  of 
Robert  Grosseteste  "who  had  especially  devoted  himself  to 
mathematics  and  experimental  science,"  and  had  studied  the 
works  of  the  Arabian  authors.  Bacon  also  travelled  abroad  and 
studied  at  the  University  of  Paris,  —  at  that  time  the  centre 
of  European  learning.  Here  he  took  the  degree  of  Doctor  of 
Theology  and  probably  also  here  became  a  Franciscan  friar.  He 
taught  at  Oxford,  where  he  had  a  kind  of  laboratory  for  alchemical 
experiments.  Doubtless  it  was  for  this  that  he  became  reputed 
as  a  worker  in  "magic"  and  the  "black  arts,"  for  in  1257  he  was 
forbidden  by  the  head  of  his  order  to  teach,  and  was  sent  to  Paris, 
where  he  underwent  great  privations.  In  1266  he  was  invited 
by  Pope  Clement  IV  to  prepare  and  send  to  him  a  treatise  on  the 
sciences,  and  within  18  months  he  had  written  and  sent  three 
important  works  —  his  Opus  Majus,  Opus  Minus,  and  Opus 
Tertium.  In  1268  he  returned  to  Oxford  and  there  composed 
several  more  works,  but  under  a  later  Pope  his  books  were  con- 
demned and  he  was  thrown  into  prison  where  he  remained  until 
about  a  year  before  his  death. 

In  Paris,  Bacon  devoted  himself  particularly  to  physical  science 
and  mathematics.  His  Opus  Majus  (1267)  contains  both  a 
summary  of  ancient  and  current  physical  science,  and  a  philosophy 
of  learning  based  on  Greek,  Roman,  and  Arabic  authorities.  He 
insisted  that  natural  science  must  have  an  experimental  basis, 
and  that  astronomy  and  the  physical  sciences  must  be  founded  on 


PROGRESS  OF  SCIENCE  TO  1450  A.D.  181 

mathematics,  "the  alphabet  of  all  philosophy."  On  the  other 
hand  he  says :  — 

We  must  consider  that  words  exercise  the  greatest  influence.  Al- 
most all  wonders  are  accomplished  through  speech.  In  words  the 
highest  enthusiasm  expresses  itself.  Therefore  words,  deeply  thought 
.  .  .  keenly  realized,  well  calculated,  and  spoken  with  emphasis,  have 
notable  power. 

Bacon  enunciated  the  essential  principles  of  calendar  reform, 
recognizing  that  the  current  plan  of  365J  days  led  to  an  error 
of  one  day  in  130  years.  He  made  an  acute  criticism  of  the  arbi- 
trary assumptions  and  the  artificial  complexity  of  the  Ptolemaic 
astronomy;  he  discussed  reflection  and  refraction,  spherical 
aberration,  rainbows,  magnifying  glasses,  and  shooting  stars; 
he  attributed  the  tides  to  the  action  of  the  lunar  rays.  In  a 
chapter  on  geography  he  "  comes  to  the  conclusion  that  the  ocean 
between  the  east  coast  of  Asia  and  Europe  is  not  very  broad. 
This  .  .  .  was  quoted  by  Columbus  in  1498.  ...  It  is  pleasant 
to  think  that  the  persecuted  English  monk,  then  two  hundred 
years  in  his  grave,  was  able  to  lend  a  powerful  hand  in  widening 
the  horizon  of  mankind."  (See  Appendix.) 

Most  of  this  remarkable  work  —  not  printed  for  nearly  500 
years  —  was  so  far  in  advance  of  the  age  that  it  not  only  failed  of 
appreciation,  but  exposed  the  author  to  accusations  of  magic,  and 
even  to  imprisonment.  In  spite  of  his  many  attainments  he 
believed  in  astrology,  in  the  doctrine  of  "  signatures  "  and  in  the 
"philosopher's  stone,"  and  "knew"  that  the  circle  had  been 
squared.  He  prophesied  ships  propelled  swiftly  by  mechanical 
means  and  carriages  without  horses.  He  repudiated  belief  in  witch- 
craft,1 and  paid  the  penalty  for  his  courage  by  many  years  in  prison. 

DANTE  ALIGHIERI  (1265-1321). —  Another  notable  scholar  of 
the  thirteenth  century  is  Dante,  the  greatest  poetical  genius 
of  the  Middle  Ages,  who  requires  our  notice  not  only  because  of 
his  influence  in  awakening  and  stimulating  the  minds  of  his  own 
and  later  times,  but  also  as  the  author  of  a  treatise  On  Water 

1  Not  merely  astrology  and  alchemy  but  even  magic  and  necromancy  were  at 
this  time  the  subjects  of  university  lecture  courses. 


182  A  SHORT  HISTORY  OF  SCIENCE 

and  the  Earth  (De  Aqua  et  Terra)  which,  according  to  himself, 
was  delivered  at  Mantua  in  1320  as  a  contribution  to  the  question, 
then  much  discussed,  "whether  on  any  part  of  the  earth's  surface 
water  is  higher  than  the  earth."  In  his  cosmology,  Dante  seems 
to  derive  from  Aristotle  and  Pliny,  without  having  attained 
familiarity  with  the  Ptolemaic  system. 

COMPUTATION  IN  THE  MIDDLE  AGES.  —  During  the  fourteenth 
century  there  was  continued  activity  in  the  gradual  dissemination 
of  Arabic  learning,  largely  through  the  medium  of  almanacs  and 
calendars,  so  that  Arabic  computations,  Euclidean  geometry,  and 
Ptolemaic  astronomy  became  widely  known.  Some  of  these 
calendars  emphasized  the  religious  side  and  gave  dates  of  church 
festivals  for  a  series  of  years,  others  specialized  in  astrology, 
medicine,  or  astronomy.  For  ecclesiastical  purposes  Roman 
numerals  were  preferred,  but  at  least  an  explanation  of  the  new 
Arabic  characters  and  their  use  was  generally  given. 

The  arithmetic  of  Boethius,  based  on  Roman  numerals,  retained 
its  vogue  in  northern  Europe  as  late  as  about  1600.  Arabic 
arithmetic,  or  algorism,  based  on  the  Liber  Abaci  of  Leonardo 
Pisano,  employing  the  decimal  scale  and  including  the  elements 
of  algebra,  came  into  general  use  among  the  Italian  merchants 
in  the  thirteenth  and  fourteenth  centuries,  though  not  without 
meeting  serious  opposition.  Outside  of  Italy,  however,  accounts 
were  kept  in  Roman  numerals  till  about  1550,  and  in  the  more 
conservative  religious  and  educational  institutions,  for  a  hundred 
years  longer.  The  Florentines  at  the  same  time  considerably 
simplified  the  classification  of  arithmetical  operations,  in  accord- 
ance with  our  modern  list :  — ••  numeration,  addition,  subtraction, 
multiplication,  division,  involution  and  evolution. 

Addition  and  subtraction  were  begun  at  the  left.  The  multi- 
plication table,  at  first  little  known,  ended  with  5x5.  For 
further  products  up  to  10  X  10,  a  system  of  finger  reckoning  was 
widely  used,  the  rule  running :  — 

Let  the  number  five  be  represented  by  the  open  hand ;  the  number 
six  by  the  hand  with  one  finger  closed ;  the  number  seven  by  the  hand 
with  two  fingers  closed;  the  number  eight  by  the  hand  with  three 


PROGRESS  OF  SCIENCE   TO   1450  A.D. 


183 


fingers  closed;  and  the  number  nine  by  the  hand  with  four  fingers 
closed.  To  multiply  one  number  by  another  let  the  multiplier  be 
represented  by  one  hand,  and  the  number  multiplied  by  the  other, 
according  to  the  above  convention.  Then  the  required  answer  is 
the  product  of  the  number  of  fingers  (counting  the  thumb  as  a  finger) 
open  in  the  one  hand  by  the  number  of  fingers  open  in  the  other  to- 
gether with  ten  times  the  total  number  of  fingers  closed.1 

Long  division  naturally  required  the  skill  of  a  mathematical 
expert.  For  example,  if  it  is  necessary  to  divide  1330  by  84 
(Ball,  p.  191)  the  Arabic  or  Persian  method  may  be  represented 
as  follows,  the  right  hand  figure  summing  up  the  whole  process: 


1 

3 

3 

0 

8 

4 

0 

1 

3 

3 

0 

8 

X 

5 

3 

0 

4 

4 

8 
\ 

9 
4 

0 

0 

1 

1 

3 

3 

0 

8 

5 

3 

0 

4 

4 

9 

0 

4 

0 

9 

0 

2 

0 

7 

0 

8 

4 

8 

4 

8 

4 

0 

1 

5 

.  The  galley  or  "  scratch  "  method  generally  employed  in  Italy 
would  take  for  the  same  problem,  the  successive  forms  (Ball,  p. 
192) : 


5 
#30(1 


4 
09 


4 
09 
#00(15 

UJ 
IrH 

8 


& 


m 

9 


;#o(i6 


1  In  modern  notation :   If  x  is  the  number  of  fingers  closed  in  one  hand,  y  the 
number  closed  in  the  other,  then 

(5  +  x)  (5  +  y)  =  (5  -  x)  (5  -  y)  +  10  (»  +  y). 


184  A  SHORT  HISTORY  OF  SCIENCE 

This  method  was  considered  simpler  than  our  modern  long 
division,  and  remained  in  use  till  the  seventeenth  century. 

The  signs  +,  — ,  -^,  and  the  use  of  decimal  fractions  belong  to 
a  somewhat  later  period. 

The  characteristics  of  the  algoristic  arithmetic  are:  (1)  the  use 
of  the  Hindu- Arabic  system  of  notation ;  (2)  the  system  of  local  value ; 
(3)  the  use  of  the  zero ;  (4)  the  entire  discarding  of  the  abacus ;  (5) 
the  combined  use  of  symbols  and  numbers  (in  reality  a  combination 
of  algebra  and  arithmetic,  as  these  terms  are  understood  to-day) ; 
and  (6)  the  introduction  into  Western  Europe  of  a  vast  amount  of 
arithmetical  material  from  the  East  by  means  of  Latin  translations 
from  Arabian  sources.  While  the  general  tendency  of  this  period 
was  to  approach  the  study  of  arithmetic  from  its  practical  and 
scientific  sides,  the  mystical  aspects  of  the  subject  —  so  popular 
in  the  earlier  periods  —  are  by  no  means  neglected.  The  fantas- 
tic treatment  of  the  properties  of  numbers  is  still  common  in  this 
age.  .  .  . 

Thus  the  beginning  of  the  thirteenth  century  marks  the  introduc- 
tion of  the  Arabian  system  of  notation  and  its  adoption  in  place  of 
both  the  Roman  notation  and  the  abacus.  This  fundamental  revolu- 
tion was  brought  about  only  gradually,  and  that  of  the  algorism  can 
be  traced  in  the  translated  literature  of  the  Hindu-Arabian  arith- 
metic. —  Abelson. 

MATHEMATICS  IN  THE  MEDIEVAL  UNIVERSITIES.  —  The  state  of 
mathematics  in  the  universities  toward  the  close  of  the  fourteenth 
century  may  be  inferred  from  the  requirements  for  the  master's 
degree  at  Prague  (1384)  and  Vienna  (1389).  The  former  included 
Sacrobosco's  Sphere,  Euclid  Books  I-VI,  optics,  hydrostatics, 
theory  of  the  lever,  and  astronomy.  Lectures  were  given  on 
arithmetic,  finger-reckoning,  almanacs,  and  Ptolemy's  Almagest. 
At  Vienna,  Euclid  I-V,  perspective,  proportional  parts,  mensu- 
ration, and  a  recent  version  of  Ptolemy  were  required.  In  Leipsic, 
however,  in  1437  and  1438  mathematical  ( ?)  lectures  were  confined 
to  astrology,  and  conditions  seem  to  have  been  much  the  same  at 
the  Italian  universities,  while  Oxford  and  Paris  probably  occupied 
an  intermediate  level. 


PROGRESS  OF  SCIENCE  TO   1450  A.D.  185 

There  can  be  no  doubt  that  at  all  times  medieval  schools  taught 
all  that  their  respective  generations  knew  of  arithmetic;  that  the 
teachers  of  arithmetic  in  the  schools  were  often  the  famous  mathe- 
maticians of  their  day ;  that  this  teaching,  since  it  kept  pace  with  the 
increase  in  the  knowledge  of  the  subject,  was  progressive  in  character, 
and  that  at  no  time,  not  even  in  the  barren  generations  at  the  close  of 
the  Middle  Ages,  when  the  scholastic  education  had  outlived  its  use- 
fulness, did  arithmetic  cease  to  be  a  subject  of  study  in  the  arts  facul- 
ties of  the  medieval  universities.  —  Abelson. 

THE  RENAISSANCE.  —  With  the  fourteenth  century  we  enter 
upon  one  of  the  most  interesting  and  noteworthy  periods  of  human 
history;  viz.  the  Renaissance.  Neither  the  term  nor  the  period 
is,  however,  sharply  defined,  the  former  signifying  an  awakening 
or  "new  birth/'  the  latter  covering  loosely  the  fourteenth  to  the 
sixteenth  centuries.  It  is  only  necessary  to  recapitulate  briefly 
some  of  the  phenomena  touched  upon  in  the  present  chapter,  to 
realize  that  the  civilization  of  the  later  Middle  Ages  has  been  under- 
going great  changes.  The  Crusades  marked  the  first  and  perhaps 
most  important  of  these,  while  the  rediscovery  or  recovery  of  the 
classics  from  Arabian  and  other  sources  in  the  eleventh  to  the  thir- 
teenth centuries,  followed  by  the  revival  of  (classical)  learning  in 
the  fourteenth  must  have  been  powerful  ferments  of  the  medieval 
scholastic  mind,  expanded  and  uplifted  as  it  was  by  the  poetical 
philosophy  of  Dante  and  challenged  by  the  naturalism  and  ration- 
alism of  Roger  Bacon. 

The  great  events  of  the  fourteenth  century  were  in  part  new, 
and  in  part  the  natural  extension  and  development  of  those  of 
the  thirteenth.  A  strange  and  appalling  natural  phenomenon  was 
the  famous  epidemic  known  as  the  "  black  death,"  a  quickly  fatal 
disease  which  carried  off  from  one  quarter  to  one  half  of  all  the 
inhabitants  of  Europe,  producing  social  changes  —  such  as  the 
rise  of  wages  —  which  are  still  felt. 

HUMANISM.  —  The  development  of  better  education  begun  in 
the  thirteenth  century  was  marked  in  the  fourteenth  by  the  found- 
ing of  many  now  famous  universities  and  colleges  and  by  that 
revival  of  ancient  learning  which  is  associated  especially  with  the 


186  A  SHORT  HISTORY  OF  SCIENCE 

name  of  Petrarch  (1304-1374).  This  revival,  while  at  first  chiefly 
literary  and  philosophical,  brought  with  it  translations  into  Latin 
—  the  current  language  of  scholars  at  that  time  —  of  Aristotle  and 
other  classical  writers  of  scientific  importance,  and  thus  aided  in 
bringing  on  a  new  birth  or  renaissance  in  science  as  well  as  in 
other  branches. 

Precisely  as  there  is  one  great  name  in  thirteenth  century 
literature,  viz.  that  of  Dante,  which  must  be  regarded  with 
attention  by  all  students  of  history,  so  in  the  fourteenth  the  name 
and  work  of  Petrarch  require  careful  consideration.  Francesco 
Petrarca,  commonly  called  Petrarch,  a  gifted  Italian  poet  and 
scholar,  greatly  promoted  the  revival  of  ancient  learning  by  insisting 
on  the  importance  and  merits  of  the  Greek  and  Roman  authors. 

Petrarch  was  less  eminent  as  an  Italian  poet  than  as  the  founder 
of  Humanism,  the  inaugurator  of  the  Renaissance  in  Italy.  .  .  . 
Standing  within  the  kingdom  of  the  Middle  Ages,  he  surveyed  the 
kingdom  of  the  modern  spirit  and,  by  his  own  inexhaustible  indus- 
try in  the  field  of  scholarship  and  study,  he  determined  what  we  call 
the  revival  of  learning.  By  bringing  the  men  of  his  own  generation 
into  sympathetic  contact  with  antiquity,  he  gave  a  decisive  impulse 
to  that  European  movement  which  restored  freedom,  self-conscious- 
ness and  the  faculty  of  progress  to  the  human  intellect.  .  .  .  He 
was  the  first  man  to  collect  libraries,  to  accumulate  coins,  to  advocate 
the  preservation  of  antique  monuments,  and  to  collate  manuscripts. 
Though  he  knew  no  Greek,  he  was  the  first  to  appreciate  its  vast  im- 
portance ;  and  through  his  influence,  Boccaccio  laid  the  earliest  founda- 
tions of  its  study.  .  .  .  For  him  the  authors  of  the  Greek  and  Latin 
world  were  living  men,  —  more  real  in  fact  than  those  with  whom  he 
corresponded;  and  the  rhetorical  epistles  he  addressed  to  Cicero, 
Seneca  and  Varro  prove  that  he  dwelt  with  them  on  terms  of 
sympathetic  intimacy.  —  Symonds. 

Rich  as  the  fourteenth  and  fifteenth  centuries  are  in  mathe- 
matical science  and  geographical  discovery,  and  in  art  and  inven- 
tion, they  are  almost  destitute  of  positive  achievement  in  natural 
science.  Doubtless  the  scientific  spirit  of  curiosity  and  inquiry 
was  alive  and  active,  but  thus  far  it  had  taken  other  directions. 


PROGRESS  OF  SCIENCE  TO   1450  A.D.  187 

ALCHEMY.  —  What  astrology  was  to  astronomy,  alchemy  was 
to  chemistry ;  viz.  the  crude  and  often  magic-working  predecessor. 
The  search  for  such  will  o'  the  wisps  as  the  "  philosopher's  stone," 
the  "elixir  of  life,"  "potable  gold"  and  the  "transmutation  of 
elements,"  is  probably  as  old  as  human  history.  The  ancients 
seem  to  have  dabbled  in  it,  the  Arabs  to  have  been  devoted  to  it, 
and  the  men  of  the  Middle  Ages,  and  even  of  the  fourteenth  and 
fifteenth  centuries,  to  have  spent  much  time  upon  it.  Alembics 
and  receivers,  "Moors'  Heads"  and  "Moors'  Noses,"  calci- 
fication, distillation,  and  the  like  typify  interesting  and  by  no 
means  fruitless  gropings  after  the  real  composition  of  things. 
The  names  of  Albertus  Magnus,  Bernard  of  Treviso,  Eck  of  Salz- 
burg, and  Basil  Valentine  are  some  which  have  come  down  to  us 
as  most  important  at  this  time,  and  as  we  read  of  the  prepara- 
tion of  the  "  spirits  of  salt "  (hydrochloric  acid),  the  calcification 
(oxidation)  of  mercury,  etc.,  we  realize  that  their  labors,  though 
often  misdirected,  were  the  prelude  to  better  things. 

THE  MARINER'S  COMPASS.  —  The  loadstone  was  certainly  known 
to  antiquity  as  a  stone  having  the  power  of  attracting  and 
carrying  a  load  of  iron,  but  its  directive  property  seems  to  have 
been  first  recognized  and  used  for  guidance  on  land  or  sea  by  the 
Chinese,  since  according  to  Humboldt,  Chinese  ships  navigated 
the  Indian  Ocean  with  the  magnetic  needle  in  the  third  century  of 
our  era.  The  Arabs  are  also  credited  with  its  invention  and  use, 
as  stated  in  the  preceding  chapter.  The  first  reference  to  it  in 
Christian  Europe  is  said  to  be  in  a  poem  by  Guyot  of  Provence, 
dated  1190,  while  references  are  also  made  to  the  compass  in 
works  of  the  thirteenth  century.  One  of  these  runs :  — 

No  master  mariner  dares  to  use  it  lest  he  should  be  suspected  of 
being  a  magician;  nor  would  the  sailors  venture  to  go  to  sea  under 
the  command  of  a  man  using  an  instrument  which  so  much  appeared 
to  be  under  the  influence  of  the  powers  below. 

It  is  probable,  however,  that  the  compass  was  first  made 
commonly  useful  to  western  Europe  early  in  the  fourteenth 
century,  by  Flavio  Gioja,  a  native  of  Amalfi,  a  small  port 


188  A  SHORT  HISTORY  OF  SCIENCE 

near  Naples  in  Italy,  who  first  poised  the  needle  on  a  pivot 
instead  of  a  card  floating  on  water,  as  had  been  the  custom 
before  his  time.  (See  page  164.) 

CLOCKS.  —  Clocks  with  wheels  seem  to  have  come  into  occa- 
sional use  from  the  twelfth  to  the  fourteenth  centuries,  and  one  of 
the  first  is  said  to  have  been  sent  by  the  Sultan  of  Egypt  in 
1232  to  the  Emperor  Frederick  II. 

It  resembled  a  celestial  globe,  in  which  the  sun,  moon  and  planets 
moved,  being  impelled  by  weights  and  wheels  so  that  they  pointed 
out  the  hour,  day  and  night,  with  certainty. 

Another  is  mentioned  as  in  Canterbury  cathedral,  while  still  an- 
other at  St.  Albans,  made  by  R.  Wallingford  who  was  abbot  there 
in  1326,  is  said  to  have  been  so  notable  "that  all  Europe  could  not 
produce  such  another."  It  remained  for  Huygens  in  the  seven- 
teenth century  to  apply  pendulums  to  clocks. 

WOOL  AND  SILK.  TEXTILES  IN  THE  MIDDLE  AGES.  —  As  an 
example  of  the  industrial  history  of  the  times  the  following  account 
of  conditions  in  Spain  is  given :  — 

The  cloth  manufactures  in  Spain  continued  to  be  of  the  coarsest 
character  until  after  the  marriage  of  Catharine  of  Lancaster  to  the 
heir  of  Castile  (1388)  when  finer  cloths  were  manufactured  and 
improved  methods  adopted.  Up  to  that  time  the  cloths  used  by 
people  of  the  higher  class  came  from  Bruges,  from  London,  and  from 
Montpellier.  James  II  of  Aragon  —  the  sovereign  of  Barcelona, 
where  there  were  at  the  time  hundreds  of  looms  at  work  making  a 
coarse  woolen  —  wished  to  send  a  present  to  the  Sultan  of  Egypt 
(1314  and  1322),  and  chose  green  cloths  from  Chalons  and  red  cloths 
from  Rheims  and  Douai,  but  sent  no  Spanish  stuff ;  while  the  stew- 
ard's accounts  of  Fernando  V  show  that  all  his  household  were  dressed 
in  garments  of  imported  stuffs.  The  great  centre  for  the  sale  of  wool 
was  at  Medina  del  Campo,  and  the  cloth  factories  of  Segovia  and 
Toledo  were  the  most  active  and  celebrated  in  Castile,  while  those 
of  Barcelona  were  the  principal  in  the  east  of  Spain.  It  is  asserted 
that  the  improvement  in  the  qualities  of  the  Spanish  cloth  after 
the  coming  of  the  Plantagenet  princess  to  Spain  was  partly  owing 
to  the  fact  that  some  herds  of  English  sheep  formed  part  of  her 


PROGRESS  OF  SCIENCE  TO  1450  A.D.  189 

dowry,  and  the  blending  of  staples  enabled  a  better  cloth  to  be 
made.  The  Flemish  weavers  mixed  Spanish  with  English  wool  for 
their  best  textures. 

During  the  Arab  domination  of  the  south,  Jaen,  Granada,  Valencia, 
and  Seville  had  been  great  centres  of  silk  culture  and  manufacture. 
Edrisi  says  that  in  the  kingdom  of  Jaen  in  the  thirteenth  century 
there  were  3000  villages  where  the  cultivation  of  the  silkworm  was 
carried  on,  while  in  Seville  there  were  6000  silk  looms,  and  Almeria 
had  800  looms  for  the  manufacture  of  fancy  brocades,  etc.  We  are 
also  told  that  a  minister  of  Pedro  the  Cruel  owned  125  chests  of  silk 
and  gold  tissue.  In  the  twelfth  century,  a  very  flourishing  trade  in 
silks,  velvets,  and  brocades  was  carried  on  with  Constantinople  and 
the  East  generally.  Even  in  the  fourteenth  and  early  fifteenth  cen- 
turies, the  silks  of  Valencia  and  the  bullion  embroideries  and  gold  and 
silver  tissues  of  Cordova  and  Toledo  were  unsurpassed  in  Christen- 
dom, though  heavily  handicapped  by  the  growing  burdens  placed 
upon  craftsmen  by  labor  laws  and  racial  prejudice,  and  the  dis- 
couragement of  luxury  by  sumptuary  regulations.  —  Hume. 

THE  INVENTION  OF  PRINTING.  —  Before  the  middle  of  the 
fifteenth  century,  printing  was  done  chiefly  from  fixed  blocks  of 
wood,  metal,  or  stone,  as  is  the  case  to-day  in  the  printing  of  en- 
gravings, wood  cuts  and  the  like.  The  introduction  of  movable 
types,  capable  of  an  almost  infinite  variety  of  combination  was 
therefore  a  forward  step  of  fundamental  importance,  since  the 
same  letter  or  picture  could  be  used  over  and  over  in  new  com- 
binations where  previously  it  could  be  used  but  once.  Until  quite 
recently,  it  was  generally  held  that  the  invention  of  the  art  of 
printing  from  movable  types  was  the  work  of  Johann  Gutenberg 
(1397-1468)  of  Mainz  on  the  Rhine,  aided  by  Johann  Faust  or 
Fust,  a  rich  citizen  of  Mainz.  Of  late,  however,  the  claim  of 
Gutenberg  has  been  much  disputed. 

The  controversy  about  the  person  and  nationality  of  the  inventor 
[of  the  art  of  printing]  and  the  place  of  invention  resembles  the  rival 
claims  of  seven  cities  to  be  the  birthplace  of  Homer.  .  .  .  The  best 
authorities  agree  on  Gutenberg.  Jacob  Wimpheling  wrote  in  1507  . . . 
*  Of  no  art  can  we  Germans  be  more  proud  than  of  the  art  of  printing, 


190 


A  SHORT  HISTORY  OF  SCIENCE 


which  made  us  the  intellectual  bearers  of  the  doctrines  of  Christianity, 
of  all  divine  and  earthly  sciences,  and  thus  benefactors  of  the  whole 
race/  —  Schaff. 

ABELSON.     The  Seven  Liberal  Arts. 

BALL.     History  of  Mathematics,  Chapters  VI,  VIII,  X. 

CAJORI.     History  of  Mathematics. 

CAJORI.     History  of  Physics. 

DRAPER.     Intellectual  Development  of  Europe. 

MUIR.     Alchemy  and  the  Beginnings  of  Chemistry. 

RASHDALL.     Universities  of  the  Middle  Ages. 

SCHAFF.     The  Renaissance. 

SYMONDS.     The  Renaissance. 

WHITE.     Warfare  of  Science  with  Theology. 


REFERENCES 

FOR 
READING 


A  MAP  OF  THE  GLOBE  IN  THE  TIME  OF  COLUMBUS 
(After  J.  H.  Robinson.    Courtesy  of  Messrs.  Ginn  &  Co.) 

'  In  1492  a  German  mariner,  Behaim,  made  a  globe  which  is  still  preserved  in  Nuremberg.  He 
did  not  know  of  the  existence  of  the  American  continents  or  of  the  vast  Pacific  Ocean.  .  .  . 
He  places  Japan  (Cipango)  where  Mexico  lies.  In  the  reproduction  many  names  are  omitted, 
and  the  outlines  of  North  and  South  America  are  sketched  in. 

—  J.  H.  ROBINSON,  Mediaeval  and  Modern  Times. 


CHAPTER  X 

A   NEW  ASTRONOMY   AND   THE   BEGINNINGS   OF 
MODERN   NATURAL   SCIENCE 

The  breeze  from  the  shores  of  Hellas  cleared  the  heavy  scholastic 
atmosphere.  Scholasticism  was  succeeded  by  Humanism,  by  the 
acceptance  of  this  world  as  a  fair  and  goodly  place  given  to  man  to 
enjoy  and  to  make  the  best  of.  In  Italy  the  reaction  became  so  great 
that  it  seemed  destined  to  put  paganism  once  more  in  the  place  of 
Christianity;  and  though  it  produced  lasting  monuments  in  art  and 
poetry,  the  earnestness  was  wanting  which  in  Germany  brought  about 
the  revival  of  science,  and  later  on  the  rebellion  against  spiritual 
tyranny.  .  .  .  Astronomy  profited  more  than  any  other  science  by 
this  revival  of  learning,  and  about  the  middle  of  the  fifteenth  century 
the  first  of  the  long  series  of  German  astronomers  arose  who  paved  the 
way  for  Copernicus  and  Kepler,  though  not  one  of  them  deserves  to 
be  called  a  precursor  of  these  heroes.  —  Dreyer. 

The  silent  work  of  the  great  Regiomontanus  in  his  chamber  at 
Nuremberg  computed  the  ephemerides  which  made  possible  the 
discovery  of  America  by  Columbus.  —  Rudio. 

The  extension  of  the  geographical  field  of  view  over  the  whole 
earth  and  the  release  of  thought  and  feeling  from  the  restrictions  of 
the  Middle  Ages  mark  a  division  of  etyual  importance  with  the  fall 
of  the  ancient  world  a  thousand  years  earlier.  —  Dannemann. 

Science  begins  to  dawn,  but  only  to  dawn,  when  a  Copernicus, 
and  after  him  a  Kepler  or  a  Galileo,  sets  to  work  on  these  raw  materials, 
and  sifts  from  them  their  essence.  She  bursts  into  full  daylight  only 
when  a  Newton  extracts  the  quintessence.  There  has  been  as  yet 
but  one  Newton ;  there  have  not  been  very  many  Keplers.  —  Tait. 

THE  AGE  OF  DISCOVERY.  —  With  the  end  of  the  fifteenth 
century  and  the  beginning  of  the  sixteenth  opens  one  of  the  most 
marvellous  chapters  in  all  history ;  viz.  the  Discovery  of  the  New 
World,  fat  about  the  same  time  further  explorations  of  the  old 
world  attained  equal  extent  and  interest.  We  have  referred  above 
(p.  174)  to  the  Discovery  of  the  East  by  the  Crusaders,  and  now 

191 


192  A  SHORT  HISTORY  OF  SCIENCE 

with  Columbus,  Magellan,  and  their  successors,  we  have  an  even 
more  pregnant  Discovery  of  the  West.  Meanwhile,  Diaz  and  da 
Gama  pushed  the  explorations  of  Prince  Henry  of  Portugal,  "  the 
Navigator,"  to  the  south,  and  in  rounding  the  Cape  of  Good 
Hope  completed  the  Discovery  of  the  South.  To  the  north,  ex- 
plorers had  already  advanced  to  regions  of  perpetual  snow  and 
ice,  so  that  in  all  directions  there  were  new  problems  of  intense 
interest  profoundly  moving  the  imagination  of  mankind. 

THE  REFORMATION.  —  Another  potent  element  was  added  to 
the  already  complex  fermentation  of  medieval  ideas  when  in  1517 
a  widespread  insurrection  began  in  the  Christian  Church,  the  most 
conservative  and  most  powerful  institution  of  the  Middle  Ages. 
This  revolution,  —  for  such  it  proved  to  be, —  with  which  the 
name  of  Luther  will  always  be  chiefly  associated,  soon  aroused 
a  wave  of  determined  opposition,  naturally  strongly  conservative, 
known  to-day  as  the  "counter-reformation,"  of  which  the  In- 
quisition was  one  instrument. 

The  increased  importance  of  the  art  of  navigation  reacted 
powerfully  on  the  underlying  sciences  of  mathematics  and  astron- 
omy, particularly  through  the  demand  for  unproved  astronomi- 
cal tables.  The  Church,  even,  had  a  strong,  if  restricted,  interest 
in  astronomy  on  account  of  the  necessity  of  more  accurate  data 
for  its  calendar. 

PIONEERS  OF  THE  NEW  ASTRONOMY.  —  Nicholas  of  Cusa 
(1401-1464),  later  Bishop  of  Brixen,  wrote  on  Learned  Ignorance, 
arguing  that  the  universe,  being  infinite  in  extent,  could  have  no 
centre,  and  that  the  earth  has  diurnal  rotation.  "It  is  now  clear 
that  the  earth  really  moves,  if  we  do  not  at  once  observe  it, 
since  we  perceive  motion  only  through  comparison  with  some- 
thing immovable."  In  mathematics  he  follows  Euclid  and 
Archimedes,  cooperating  in  a  translation  of  the  latter  from 
Greek  into  Latin,  and  dealing  with  the  squaring  of  the  circle. 

He  makes  a  map  of  the  known  world,  using  central  projection. 
He  is  said  to  have  determined  areas  of  irregular  boundary  by  the 
then  novel  method  of  cutting  them  out  and  weighing,  and  is  one 
of  the  first  to  emphasize  the  importance  of  measurement  in  all 


A  NEW  ASTRONOMY  193 

investigations.  He  showed  independence  of  thinking,  but  his 
astronomical  theories  were  too  little  developed  —  and  too  specula- 
tive —  to  constitute  real  progress  in  an  age  not  yet  quite  ripe  for 
their  reception. 

Peurbach  (1423-1461),  who  had  as  a  youth  met  Nicholas  of 
Cusa  in  Rome,  became  professor  of  astronomy  and  mathematics 
in  Vienna  and  has  been  called  "  the  founder  of  observational  and 
mathematical  astronomy  in  the  West/'  Recognizing  the  imper- 
fections of  the  Alfonsine  tables  he  published  a  new  edition  of 
the  Almagest  with  tables  of  natural  sines  —  instead  of  chords  — 
computed  for  every  ten  minutes.  He  depended  mainly,  however, 
on  imperfect  Arabic  translations. 

His  more  eminent  pupil  and  successor,  Johann  Miiller,  of 
Konigsberg,  better  known  as  Regiomontanus  (1436-1476),  was 
the  most  distinguished  scientific  man  of  his  time.  After  the 
fall  of  Constantinople  he  was  among  the  first  to  avail  himself  of 
the  opportunities  for  more  direct  acquaintance  with  the  works 
of  Archimedes,  Apollonius,  and  Diophantus.  For  the  defective 
version  of  the  Almagest  which  had  come  through  Arabic 
channels  he  substituted  the  Greek  original,  while  his  tables,  pub- 
lished in  1475,  were  important  both  for  astronomy  and  for  the 
voyages  of  discovery  of  Vasco  da  Gama,  Vespucci,  and  Colum- 
bus. These  tables  covered  the  period  1473  to  1560,  giving  sines 
for  each  minute  of  arc,  longitudes  for  sun  and  moon,  latitude  for 
the  moon,  and  a  list  of  predicted  eclipses  from  1475  to  1530.  An- 
other work  on  astrology  includes  a  table  of  natural  tangents  for 
each  degree.  A  wealthy  merchant  of  Nuremberg  erected  an 
elaborately  equipped  observatory  for  Regiomontanus,  and  the 
printing-press  recently  established  there  became  the  most  impor- 
tant in  Germany.  Accepting,  however,  a  summons  to  Rome  to 
reform  the  calendar,  he  was  murdered  at  the  age  of  40. 

His  De  Triangulis  (1464)  is  the  earliest  modern  trigonometry. 
Four  of  its  five  books  are  devoted  to  plane  trigonometry,  the 
other  to  spherical.  He  determines  triangles  from  three  given 
conditions,  using  sines  and  cosines,  and  employs  quadratic  equa- 
tions successfully  in  some  of  his  solutions.  One  of  his  problems 


194  A  SHORT  HISTORY  OF  SCIENCE 

is  "to  determine  a  triangle  when  the  difference  of  two  sides,  the 
perpendicular  on  the  base,  and  the  difference  between  the  seg- 
ments into  which  the  base  is  divided  are  given :  i.e.  a  —  b,  a  sin  B, 
a  cos  B  —  b  cos  A  are  known ;  to  find,  a,  b,  c,  A,  B,  (7."  An- 
other is  to  construct  from  four  given  lines  a  quadrilateral  which 
can  be  inscribed  in  a  circle. 

CONDITIONS  NECESSARY  FOR  PROGRESS.  —  The  genius  of 
Hipparchus  and  Ptolemy  had  brought  Greek  astronomy  to  its 
culmination.  Higher  it  could  not  rise  until  three  conditions 
should  be  fulfilled,  even  though  here  and  there  the  heliocentric 
hypothesis  might  be  adopted  through  an  unsupported  inspiration 
of  individuals.  First,  there  must  be  better  astronomical  instru- 
ments and  more  accurate  observations,  extended  over  long  periods. 
Second,  there  must  be  improved  methods  of  mathematical  com- 
putation for  the  reduction  and  interpretation  of  these  observations. 
Third,  there  must  be  substantial  progress  towards  clear  thinking 
as  to  the  fundamental  facts  and  laws  of  motion.  These  conditions 
were  met  one  after  another  during  the  sixteenth  and  seventeenth 
centuries  by  an  extraordinary  series  of  men  of  genius,  among  whom 
the  chief  were  Copernicus,  Tycho  Brahe,  Kepler,  Galileo,  and 
Newton.  Their  work  constitutes  a  great  part  of  the  history  of 
science  during  these  two  centuries  —  and  one  of  the  most  won- 
derful chapters  of  all  time. 

Of  these  five,  Copernicus  and  Kepler  were  predominantly  inter- 
ested on  the  mathematical  and  theoretical  side,  Tycho  Brahe  was 
a  great  observer,  Galileo  combined  experimental  and  observa- 
tional skill  with  a  new  appreciation  of  physical  laws,  while  Newton, 
building  on  the  foundation  laid  by  all  the  others,  made  a  magnifi- 
cent synthesis  of  their  results  into  a  rational  and  consistent  mathe- 
matical theory  of  the  solar  system.  These  five  represent  Poland, 
South  Germany,  Denmark,  Italy,  and  England.  Scientific  progress 
is  no  longer  localized  or  dependent  on  princely  patronage.  It  has 
now  become  international. 

NICOLAUS  COPERNICUS  (1473-1543)  was  born  in  the  remote 
little  city  of  Thorn  on  the  Vistula,  and  having  relatives  in  the 
Church,  prepared  himself  for  an  ecclesiastical  career.  This  led 


A  NEW  ASTRONOMY  195 

him,  after  medical  study  at  Cracow,  first  to  the  university  of 
Vienna,  then  to  the  chief  Italian  universities,  Bologna,  Padua, 
Ferrara,  and  Rome,  where  he  found  opportunity  to  cultivate  his 
mathematical  talents  and  to  master  what  was  then  known  of 
astronomy.  He  became  canon  at  Frauenburg  in  his  native  land 
in  1497,  and  from  1512  until  his  death  thirty  years  later,  was 
settled  there,  rendering  varied  public  services,  and  practising 
gratuitously,  as  needful,  the  medical  art  he  had  also  learned.  At 
the  same  time  he  found  it  possible  to  devote  much  attention  to 
astronomical  studies. 

In  his  study  of  the  classical  writers  he  came  upon  a  statement 
that  certain  Pythagorean  philosophers  explained  the  phenomena 
of  the  daily  and  yearly  motions  of  the  heavenly  bodies  by  sup- 
posing the  earth  itself  to  rotate  on  its  axis  and  to  have  also  an 
orbital  motion. 

'  Occasioned  by  this,  I  also  began  to  think  of  a  motion  of  the  earth, 
and  although  the  idea  seemed  absurd,  still,  as  others  before  me  had 
been  permitted  to  assume  certain  circles  in  order  to  explain  the  motions 
of  the  stars,  I  believed  it  would  readily  be  permitted  me  to  try  whether 
on  the  assumption  of  some  motion  of  the  earth  better  explanations 
of  the  revolutions  of  the  heavenly  spheres  might  not  be  found.  And 
thus  I  have,  assuming  the  motions  which  I  in  the  following  work  at- 
tribute to  the  earth,  after  long  and  careful  investigation,  finally  found 
that  when  the  motions  of  the  other  planets  are  referred  to  the  circu- 
lation of  the  earth  and  are  computed  for  the  revolution  of  each  star, 
not  only  do  the  phenomena  necessarily  follow  therefrom,  but  the 
order  and  magnitude  of  the  stars  and  all  their  orbs  and  the  heaven 
itself  are  so  connected  that  in  no  part  can  anything  be  transposed 
without  confusion  to  the  rest  and  to  the  whole  universe/  —  Dreyer. 

1 1  made  every  effort  to  read  anew  all  the  books  of  philosophers  I 
could  obtain,  in  order  to  ascertain  if  there  were  not  some  one  of 
them  of  the  opinion  that  other  motions  of  the  heavenly  bodies  existed 
than  are  assumed  by  those  who  teach  mathematical  sciences  in  the 
schools.  So  I  found  first  in  Cicero  that  Hicetas  of  Syracuse  believed 
the  earth  moved.  Afterwards  I  found  also  in  Plutarch  that  others 
were  likewise  of  this  opinion.  .  .  .  Starting  thence  I  began  to  re- 
flect on  the  mobility  of  the  earth.'  —  Timerding. 


196  A  SHORT  HISTORY  OF  SCIENCE 

Copernicus  was  not  a  great  observational  astronomer.  His 
instruments  were  poor,  his  eyesight  not  keen,  his  location  un- 
favorable for  clear  skies.  His  recorded  observations  are  few, 
chiefly  of  eclipses  or  oppositions  of  planets,  and  of  no  high  degree 
of  accuracy.  His  interest  and  genius  lay  rather  in  the  direction 
of  profound  analysis  and  careful  mathematical  revision  of  the 
current  geocentric  theory,  practically  unchanged  since  its  formu- 
lation by  Ptolemy  thirteen  centuries  earlier.  Unfortunately  the 
conditions  of  the  time  were  adverse  to  the  publication  of  so  radical 
an  innovation  as  a  heliocentric  theory  of  the  solar  system;  nor 
was  Copernicus  ever  greatly  interested  in  any  publication  of  his 
results,  being  both  indifferent  to  reputation  and  averse  to  con- 
troversy. 

'  The  scorn, '  he  says,  '  which  I  had  to  fear  in  consequence  of  the 
novelty  and  seeming  unreasonableness  of  my  ideas,  almost  moved  me 
to  lay  the  completed  work  aside/ 

Moreover,  he  realized  the  futility  of  publishing  his  revolu- 
tionary theories  until  he  should  have  buttressed  them  with  a 
planetary  system  so  completely  worked  out  that  its  superiority 
to  the  long-intrenched  Ptolemaic  system  should  be  unquestionable 
—  a  herculean,  if  congenial  labor.  Nevertheless,  he  gradually 
formulated  his  astronomical  system  in  manuscript,  and  about 
1529  issued  a  Commentariolus  giving  an  outline  of  his  theory, 
which  thus  became  gradually  but  vaguely  known  to  scholars. 
Ten  years  later  George  Joachim  —  RTieticus  —  a  young  professor 
of  mathematics  from  the  Lutheran  university  of  Wittenberg, 
visited  Copernicus,  eager  to  learn  more  of  the  new  doctrine. 
The  Lutheran  church  was  not  more  hospitable  than  the  Roman 
Catholic  to  scientific  novelty  and  Luther  himself  called  Copernicus 
a  fool.  v  v 

DE  REVOLUTIONIBUS. — In  1540  appeared  the  Prima  Narratio 
by  Rheticus  containing  a  considerable  admixture  of  astrology,  and 
in  1543  the  immortal  De  Revolutionibiw  Orbium  Celestium,  a  copy 
reaching  Copernicus,  it  is  said,  on  his  death-bed.  He  begins  with 
certain  postulates :  first,  that  the  universe  is  spherical ;  second,  that 


A  NEW  ASTRONOMY  197 

the  earth  is  spherical ;  third,  that  the  motions  of  the  heavenly  bodies 
are  uniform  circular  motions  or  compounded  of  such  motions. 
The  slender  basis  for  the  first  and  third  of  these  may  be  inferred 
from  his  statement  in  regard  to  certain  hypothetical  causes  of 
want  of  uniformity :  — 

Both  of  which  things  the  intellect  shrinks  from  with  horror,  it 
being  unworthy  to  hold  such  a  view  about  bodies  which  are  con- 
stituted in  the  most  perfect  order. 

He  makes  the  relative  character  of  the  motions  involved  of 
fundamental  importance.  In  his  own  words  :  — 

For  all  change  in  position  which  is  seen  is  due  to  a  motion  either 
of  thfe  observer  or  of  the  thing  looked  at,  or  to  changes  in  the  position 
of  both,  provided  that  these  are  different.  For  when  things  are 
moved  equally  relatively  to  the  same  things,  no  motion  is  perceived, 
as  between  the  object  seen  and  the  observer. 

Thus  the  daily  revolution  of  Jhn,  moon,  and  stars  about  a  station- 
ary earth  would  have  the  same  apparent  effect  as  rotation  of  the 
earth  in  the  opposite  direction  about  its  own  axis,  and  the  ap- 
parent yearly  motion  of  the  sun  about  the  earth  is  equivalent  to 
an  orbital  motion  of  the  latter. 

'It  is/  he  says,  'more  probable  that  the  earth  turns  about  its 
axis  than  that  the  planets  at  their  various  distances,  the  comets  sweep- 
ing through  space,  and  the  endless  multitude  of  the  fixed  stars,  describe 
the  same  regular  daily  motion  about  the  earth.' 

The  apparent  irregularities  in  the  motions  of  the  five  known 
planets  had  been  a  perpetual    stumbling-block  to  the    ancient 
\  astronomers,  requiring  more  and  more  complicated  hypotheses  for 
'  their  explanations  as  accuracy  of  observations  increased.      The 
heliocentric  theory  of  Copernicus,  inaccurate  as  it  was  in  some 
respects,  afforded  a  simple  explanation  of  the  fact  that  Mercury 
and   Venus  seem  merely  to  oscillate  east  and  west  of  the  sun, 
while  Mars,  Jupiter,  and  Saturn  recede  indefinitely  from  it,  ex- 
hibiting also  periodic  reversals  of  the  direction  of  their  motion. 


198 


A  SHORT  HISTORY  OF  SCIENCE 


The  new  explanation  obviously  accounted  also  for  the  variations 
in  the  brightness  of  these  planets. 

"  '  It  is  certain, '  he  says, '  that  Saturn,  Jupiter  and  Mars  are  always 
nearest  the  earth  when  they  rise  in  the  evening,  that  is  when  they  are 
in  opposition  to  the  sun,  as  thp  earth  is  situated  between  them  and 


THE  COPEBNICAN  SYSTEM 

the  sun.  On  the  contrary,  Mars  and  Jupiter  are  farthest  from  the 
earth  when  they  set  in  the  evening,  the  sun  lying  between  them  and 
us.  This  proves  sufficiently  that  the  sun  is  the  centre  of  their  orbits, 
as  of  those  of  Venus  and  Mercury.  Since  thus  all  planets  move 
about  one  centre  it  is  necessary  that  the  space  which  remains  between 
the  circles  of  Venus  and  Mars,  contain  the  earth  and  its  accompanying 
moon/ 

He  is,  therefore,  not  afraid  to  maintain  that  the  earth  with  the 
moon  encircling  it,  traverses  a  great  circle  in  its  annual  motion 
among  the  planets  about  the  sun.  The  universe,  however,  is  so 
vast,  that  the  distances  of  the  planets  from  the  sun  are  insignificant 


A  NEW  ASTRONOMY  199 

in  comparison  with  that  of  the  sphere  of  the  stars.  He  holds 
all  this  easier  of  comprehension,  than  if  the  mind  is  confused  by 
an  almost  endless  mass  of  circles,  as  is  necessary  for  those  who  put 
the  earth  in  the  centre  of  the  universe. 

'So  in  fact  the  sun  seated  on  the  royal  throne  guides  the  family 
of  planets  encircling  it.  We  find  thus  in  this  arrangement  a  har- 
monious connection  not  otherwise  realized.  For  here  one  can  see 
why  the  forward  and  backward  motions  of  Jupiter  seem  greater  than 
those  of  Saturn  and  smaller  than  those  of  Mars.' 

His  adherence  to  the  Greek  assumption  of  uniform  circular 
motion  leaves  him  still  under  the  necessity  of  retaining  an  elabo- 
rate system  of  epicycles,  but  he  rejects  Ptolemy's  equant. 

...  He  his  fabric  of  the  heavens 
Hath  left  to  their  disputes,  perhaps  to  move 
His  laughter  at  their  quaint  opinions  wide ; 
Hereafter  when  they  come  to  model  heaven 
And  calculate  the  stars,  how  will  they  wield 
The  mighty  frame !  how  build,  unbuild,  contrive 
To  save  appearances  !  how  gird  the  sphere 
With  centric  and  eccentric  scribbled  o'er, 
Cycle  in  epicycle,  orb  in  orb ! 

—  Milton,  Paradise  Lost,  VIII. 

The  epicycles  of  Copernicus  numbered  however  but  34, — 
sufficing  "to  explain  the  whole  construction  of  the  world  and  the 
whole  dance  of  the  planets  "  —  against  the  79  to  which  the  Ptole- 
maic theory  had  gradually  attained.  The  completeness  of  mathe- 
matical detail  with  which  the  whole  theory  is  worked  out  can  not 
here  be  adequately  described.  He  includes  so  much  trigonometry 
as  his  astronomical  work  requires,  also  a  revision  of  Ptolemy's  star 
catalogue.  He  computes  a  very  accurate  value  of  the  equinoctial 
precession,  and  interprets  this  correctly  as  due  to  a  slow  conical 
motion  of  the  earth's  axis,  like  that  of  a  top  coming  to  rest. 

Copernicus  estimates  the  relative  sizes  of  moon,  earth  and 


200  A  SHORT  HISTORY  OF  SCIENCE 

sun  as  1 : 43  : 6937,  and  the  distance  from  earth  to  sun  —  according 
to  the  method  of  Aristarchus  —  at  about  1200  earth-radii,  that 
is  about  ^y  of  the  actual. 

Revolutionary  as  were  the  theories  expounded  by  Copernicus 
they  were  not  clothed  in  such  popular  form  as  to  occasion  imme- 
diate or  general  controversy.  In  dedicating  his  work  to  the 
Pop§4  Copernicus  says  in  substance :  — 

It  seems  to  me  that  the  church  can  derive  some  advantage  from 
my  labors.  Under  Leo  X  indeed  the  rectification  of  the  calendar 
was  not  possible,  since  the  length  of  the  year  and  the  motions  of 
the  sun  and  moon  were  not  exactly  determined.  I  have  sought  to 
determine  these  more  closely.  What  I  have  accomplished,  I  leave 
to  the  judgment  of  your  Holiness,  and  of  the  learned  mathemati- 
cians. (See  Appendix.) 

\ 

Moreover  criticism  was  in  considerable  measure  disarmed  by 
a  fraudulent  preface  inserted  by  Osiander,  a  Lutheran  theologian 
of  Nuremberg,  to  whom  the  care  of  publication  had  been  par- 
tially intrusted  by  Rheticus.  In  this  preface,  ostensibly  by 
Copernicus  himself,  it  is  stated,  — 

that  though  many  will  take  offence  at  the  doctrine  of  the  earth's 
motion,  it  will  be  found  on  further  consideration  that  the  author 
does  not  deserve  blame.  For  the  object  of  an  astronomer  is  to 
put  together  the  history  of  the  celestial  motions  from  careful  ob- 
servations, and  then  to  set  forth  their  causes  or  hypotheses  about 
them,  if  he  cannot  find  the  real  causes,  so  that  those  motions  can  be 
computed  on  geometrical  principles.  But  it  is  not  necessary  that 
his  hypotheses  should  be  true,  they  need  not  even  be  probable;  it 
is  sufficient  if  the  calculations  founded  on  them  agree  with  the  obser- 
vations. Nobody  would  consider  the  epicycle  of  Venus  probable, 
as  the  diameter  of  the  planet  in  its  perigee  ought  to  be  four  times  as 
great  as  in  the  apogee,  which  is  contradicted  by  the  experience  of  all 
times.  Science  simply  does  not  know  the  cause  of  the  apparently 
irregular  motions,  and  an  astronomer  will  prefer  the  hypothesis  which 
is  most  easily  understood.  Let  us  therefore  add  the  following  new 
hypotheses  to  the  old  ones,  as  they  are  admirable  and  simple,  but 


A  NEW  ASTRONOMY  201 

nobody  must  expect  certainty  about  astronomy,  for  it  cannot  give  it ; 
and  whoever  takes  for  truth  what  has  been  designed  for  a  different 
purpose,  will  leave  this  science  as  a  greater  fool  than  he  was  when 
he  approached  it. 

INFLUENCE  OF  COPERNICUS. — The  publication  of  De  Revoliir 
tionibus  was  naturally  a  powerful  stimulus  to  astronomical  and 
mathematical  studies.  Thus  Rheticus,  whose  relations  to  Coper- 
nicus had  been  so  fruitful,  calculated  a  new  and  extensive  set 
of  mathematical  tables,  while  Reinhold,  who  had  hailed  Coper- 
nicus as  a  new  Ptolemy,  published  astronomical  tables  —  the 
Prutenic  or  Prussian  —  on  the  basis  of  Copernicus'  work,  superior 
to  the  Alfonsine,  previously  current. 

Before  the  new  doctrine  should  be  completely  justified  or  the 
reverse,  it  was  necessary  that  certain  mechanical  notions  should 
be  clarified,  and  that  more  accurate  observational  data  should  be 
systematically  collected.  Copernicus  had  based  his  imposing  \ 
structure  on  a  very  slender  foundation  of  actual  fact,  and  had  { 
professed  his  complete  satisfaction  if  his  theoretical  results  should 
come  within  ten  minutes  of  the  observed  positions  of  the  planets,  — 
a  degree  of  accuracy  which  he  did  not,  in  fact,  attain.  On  the  other 
hand,  he  could  indeed  answer,  but  not  rise  entirely  above,  the 
traditional  notions  that  the  four  elements  of  the  ancients  must 
have  rectilinear,  the  heavenly  bodies  circular,  motion ;  also,  that  if 
the  earth  rotated  in  twenty-four  hours,  loose  bodies  would  long 
since  have  been  thrown  off,  falling  bodies  would  not  fall,  and  clouds 
would  always  be  left  behind  in  the  west. 

As  suggested  by  Dreyer :  — 

It  is  interesting,  though  useless,  to  speculate  on  what  would  have 
been  the  chances  of  immediate  success  of  the  work  of  Copernicus  if 
it  had  appeared  fifty  years  earlier.  Among  the  humanists  there 
certainly  was  considerable  freedom  of  thought,  and  they  would  not 
have  been  prejudiced  against  the  new  conception  of  the  world  because 
it  upset  the  medieval  notion  of  a  set  of  planetary  spheres  inside  the 
empyrean  sphere,  with  places  allotted  for  the  hierarchy  of  angels. 
If  one  of  the  leaders  of  the  Church  (at  least  in  Italy)  at  the  beginning 


202  A  SHORT  HISTORY  OF  SCIENCE 

of  the  sixteenth  century  had  been  asked  whether  the  idea  of  the  earth 
moving  through  space  was  not  clearly  heretical,  he  would  probably 
merely  have  smiled  at  the  innocence  of  the  enquirer  and  have  answered 
in  the  words  of  Pomponazzi  that  a  thing  might  be  true  in  philosophy 
and  yet  false  in  theology.  But  the  times  had  changed.  The  sun  of 
the  Renaissance  had  set  when,  in  1527,  the  hordes  of  the  Constable  of 
Bourbon  sacked  and  desecrated  Rome ;  the  Reformation  had  put  an 
end  to  the  religious  and  intellectual  solidarity  of  the  nations,  and  the 
contest  between  Rome  and  the  Protestants  absorbed  the  mental 
energy  of  Europe.  During  the  second  half  of  the  sixteenth  century 
science  was  therefore  very  little  cultivated,  and  though  astronomy  and 
astrology  attracted  a  fair  number  of  students  (among  whom  was  one 
of  the  first  rank),  still  theology  was  thought  of  first  and  last.  And 
theology  had  come  to  mean  the  most  literal  acceptance  of  every  word 
of  Scripture ;  to  the  Protestants  of  necessity,  since  they  denied  the 
authority  of  Popes  and  Councils,  to  the  Roman  Catholics  from  a 
desire  to  define  their  doctrines  more  narrowly  and  to  prove  how  un- 
justified had  been  the  revolt  against  the  Church  of  Rome.  There 
was  an  end  of  all  talk  of  Christian  Renaissance  and  of  all  hope  of  rec- 
onciling faith  and  reason ;  a  new  spirit  had  arisen  which  claimed 
absolute  control  for  Church  authority.  Neither  side  could  therefore 
be  expected  to  be  very  cordial  to  the  new  doctrine. 

Robert  Recorde,  in  his  Pathway  to  Knowledge  (1551),  has  his 
"Master"  state  to  a  "scholar  " : 

'Eraclides  Ponticus,  a  great  philosopher,  and  two  great  clerkes  of 
Pythagoras  schole,  Philolaus  and  Ecphantus,  were  of  the  contrary 
opinion,  but  also  Nicias  Syracusius  and  Aristarchus  Samius  seem  with 
strong  arguments  to  approve  it.'  After  saying  that  the  matter  is  too 
difficult  and  must  be  deferred  till  another  time,  the  Master  states 
that  '  Copernicus,  a  man  of  great  learning,  of  muche  experience  and 
of  wondrefull  diligence  in  obseruation,  hathe  renewed  the  opinion  of 
Aristarchus  Samius,  and  affirmeth  that  the  earthe  not  only  moueth 
circularlye  about  his  own  centre,  but  also  may  be,  yea  and  is  con- 
tinually out  of  the  precise  centre  38  hundredth  thousand  miles ;  but 
bicause  the  vnderstanding  of  that  controuersy  dependeth  of  prof  ounder 
knowledge  than  in  this  introduction  may  be  vttered  conueniently,  I  will 
let  it  passe  tyll  some  other  time/ 


A  NEW  ASTRONOMY  203 

A  little  later  Francis  Bacon  writes :  — 

'  In  the  system  of  Copernicus  there  are  many  and  grave  difficulties ; 
for  the  threefold  motion  with  which  he  encumbers  the  earth  is  a  serious 
inconvenience,  and  the  separation  of  the  sun  from  the  planets,  with 
which  he  has  so  many  affections  in  common,  is  likewise  a  harsh  step ; 
and  the  introduction  of  so  many  immovable  bodies  into  nature,  as  when 
he  makes  the  sun  and  the  stars  immovable,  the  bodies  which  are  pecul- 
iarly lucid  and  radiant,  and  his  making  the  moon  adhere  to  the  earth 
in  a  sort  of  epicycle,  and  some  other  things  which  he  assumes,  are 
proceedings  which  mark  a  man  who  thinks  nothing  of  introducing  fic- 
tions of  any  kind  into  nature,  provided  his  calculations  turn  out  well/ 

Bacon  himself  was  very  ignorant  of  all  that  had  been  done  by 
mathematics ;  and,  strange  to  say,  he  especially  objected  to  astronomy 
being  handed  over  to  the  mathematicians.  Leverrier  and  Adams, 
calculating  an  unknown  planet  into  a  visible  existence  by  enormous 
heaps  of  algebra,  furnish  the  last  comment  of  note  on  this  specimen 
of  the  goodness  of  Bacon's  view.  .  .  .  Mathematics  was  beginning 
to  be  the  great  instrument  of  exact  inquiry ;  Bacon  threw  the  science 
aside,  from  ignorance,  just  at  the  time  when  his  enormous  sagacity, 
applied  to  knowledge,  would  have  made  him  see  the  part  it  was  to  play. 
If  Newton  had  taken  Bacon  for  his  master,  not  he,  but  somebody  else, 
would  have  been  Newton.  —  De  Morgan. 

Copernicus  cannot  be  said  to  have  flooded  with  light  the  dark* 
places  of  nature  —  in  the  way  that  one  stupendous  mind  subsequently 
did  —  but  still,  as  we  look  back  through  the  long  vista  of  the  history 
of  science,  the  dim  Titanic  figure  of  the  old  monk  seems  to  rear  itself 
out  of  the  dull  flats  around  it,  pierces  with  its  head  the  mists  that  over- 
shadow them,  and  catches  the  first  gleam  of  the  rising  sun,  .  .  . 

Like  some  iron  peak,  by  the  Creator 

Fired  with  the  red  glow  of  the  rushing  morn. 

—  E.  J.  C.  Morton. 

TYCHO  BRAKE  (1546-1601).  —  The  first  great  need  of  the  new 
Copernican  astronomy  —  adequate  and  accurate  data  —  was  soon 
to  be  supplied  by  Tycho  Brahe,  bom  in  1546  of  a  noble  Danish 
family.  While  a  student  at  the  University  of  Copenhagen  his 
interest  in  astronomy  was  enlisted  by  an  eclipse,  and  later,  at 
Leipsic,  he  persisted  in  devoting  to  his  new  avocation  the  time 


204  A  SHORT  HISTORY  OF  SCIENCE 

and  attention  he  was  expected  to  give  to  subjects  more  highly 
esteemed  for  a  man  of  birth  and  fortune. 

From  a  lunar  eclipse  which  took  place  while  he  was  at  Leipsic, 
Tycho  foretold  wet  weather,  which  also  turned  out  to  be  correct. 

Here,  too,  he  began  his  life  work  of  procuring  and  improving  the 
best  instruments  for  astronomical  observations,  at  the  same  time 
testing  and  correcting  their  errors.  Returning  to  Denmark  from 
travels  in  Germany,  his  predilection  for  astronomy  was  powerfully 
stimulated  by  the  appearance  in  the  constellation  Cassiopeia,  in 
November,  1572,  of  a  brilliant  new  star,  which  remained  visible  for 
16  months.  The  great  importance  attached  to  this  occurrence  by 
Tycho  and  his  contemporaries  was  due  to  the  evidence  it  afforded 
against  the  truth  of  the  Aristotelian  conviction  that  the  heavens 
were  immutable,  since  Tycho's  careful  observations  showed  that 
the  star  must  certainly  be  more  distant  than  the  moon,  and  that  it 
had  no  share  in  the  planetary  motions.  He  reluctantly  published 
an  account  of  the  new  star,  expressing  still  his  adherence  to 
the  current  pre-Copernican  notions  of  crystalline  spheres  for  the 
different  heavenly  bodies  and  of  atmospheric  comets,  all  com- 
bined with  astrological  reflections  and  inferences,  as  illustrated  by 
the  following  passages  from  Dreyer's  biography :  — 

The  star  was  at  first  like  Venus  and  Jupiter,  and  its  effects  will 
therefore  first  be  pleasant ;  but  as  it  then  became  like  Mars,  there  will 
next  come  a  period  of  wars,  seditions,  captivity,  and  death  of  princes 
and  destruction  of  cities,  together  with  dryness  and  fiery  meteors  in 
the  air,  pestilence,  and  venomous  snakes.  Lastly,  the  star  became 
like  Saturn,  and  there  will  therefore,  finally,  come  a  time  of  want, 
death,  imprisonment,  and  all  kinds  of  sad  things. 

As  the  star  seen  by  the  wise  men  foretold  the  birth  of  Christ, 
the  new  one  was  generally  supposed  to  announce  His  last  coming 
and  the  end  of  the  world. 

That  an  unusual  celestial  phenomenon  occurring  at  that  particular 
moment  should  have  been  considered  as  indicating  troublous  times, 
is  extremely  natural  when  we  consider  the  state  of  Europe  in  1573. 
The  tremendous  rebellion  against  the  Papal  supremacy,  which  for  a 
long  time  had  seemed  destined  to  end  in  the  complete  overthrow  of 


TYCHO  BRAKE'S  QUADRANT. 


;A  NEW  ASTRONOMY  205 

the  latter,  appeared  now  to  have  reached  its  limit,  and  many  people 
thought  that  the  tide  had  already  commenced  to  turn. 

Tycho  considered  that  the  new  star  was  formed  of  *  celestial 
matter/  not  differing  from  that  of  which  the  other  stars  are  composed, 
except  that  it  was  not  of  such  perfection  or  solid  composition  as  in 
the  stars  of  permanent  duration.  It  was  therefore  gradually  dissolved 
and  dwindled  away.  It  became  visible  to  us  because  it  was  illuminated 
by  the  sun,  and  the  matter  of  which  it  was  formed  was  taken  from  the 
Milky  Way,  close  to  the  edge  of  which  the  star  was  situated,  and  in 
which  Tycho  believed  he  could  now  see  a  gap  or  hole  which  had  not 
been  there  before. 

But  the  star  had  a  truer  mission  than  that  of  announcing  the 
arrival  of  an  impossible  golden  age.  It  roused  to  unwearied  exertions 
a  great  astronomer,  it  caused  him  to  renew  astronomy  in  all  its  branches 
by  showing  the  world  how  little  it  knew  about  the  heavens;  his 
work  became  the  foundation  on  which  Kepler  and  Newton  built  their 
glorious  edifice,  and  the  star  of  Cassiopeia  started  astronomical  science 
on  the  brilliant  career  which  it  has  pursued  ever  since,  and  swept 
away  the  mist  that  obscured  the  true  system  of  the  world.  As  Kepler 
truly  said,  'If  that  star  did  nothing  else,  at  least  it  announced  and 
produced  a  great  astronomer.' 

At  the  same  time  the  book  bears  witness  to  the  soberness  of  mind 
which  distinguishes  him  from  most  of  the  other  writers  on  the  subject 
of  the  star.  His  account  of  it  is  very  short,  but  it  says  all  there 
could  be  said  about  it  —  that  it  had  no  parallax,  that  it  remained 
immovable  in  the  same  place,  that  it  looked  like  an  ordinary  star  — 
and  it  describes  the  star's  place  in  the  heavens  accurately,  and  its 
variations  in  light  and  color.  Even  though  Tycho  made  some  re- 
marks about  the  astrological  significance  of  the  star,  he  did  so  in  a 
way  which  shows  that  he  did  not  himself  consider  this  the  most  valu- 
able portion  of  his  work.  To  appreciate  his  little  book  perfectly,  it 
is  desirable  to  glance  at  some  of  the  other  numerous  books  and  pam- 
phlets which  were  written  about  the  star,  and  of  most  of  which 
Tycho  himself  has  in  his  later  work  given  a  very  detailed  analysis. 

In  1575  Tycho  obtained  while  travelling  a  copy  of  Copernicus' 
Commentariolus,  and  in  the  following  year  received  from  King 
Frederick  II  the  island  of  Hveen,  with  funds  for  the  maintenance 
of  an  observatory  upon  it.  As  to  the  former  his  opinion  is  that 


206  A  SHORT  HISTORY  OF  SCIENCE 

*  The  Ptolemean  system  was  too  complicated,  and  the  new  one 
which  that  great  man  Copernicus  had  proposed,  following  in  the 
footsteps  of  Aristarchus  of  Samos,  though  there  was  nothing  in  it 
contrary  to  mathematical  principles,  was  in  opposition  to  those  of 
physics,  as  the  heavy  and  sluggish  earth  is  unfit  to  move,  and  the 
system  is  even  opposed  to  the  authority  of  Scripture/ 

—  Dreyer,  Tycho  Brahe. 

URANIBORG. — The  observatory  of  Uraniborg  —  the  castle  of 
the  heavens  —  at  Hveen  was  an  extraordinary  establishment. 

In  a  large  square  inclosure  oriented  according  to  the  points  of 
the  compass,  were  several  observatories,  a  library,  laboratory, 
living-rooms  and,  later,  workshops,  a  paper-mill  and  printing- 
press,  and  even  underground  observatories.  The  whole  estab- 
lishment was  administered  with  lavish  extravagance,  while  Tycho 
was  neither  careful  of  his  obligations  nor  free  from  arbitrary  ar- 
rogance in  his  personal  and  administrative  relations.  In  spite  of 
these  difficulties  "  a  magnificent  series  of  observations,  far  transcend- 
ing in  accuracy  and  extent  anything  that  had  been  accomplished 
by  his  predecessors"  was  carried  on  for  not  less  than  21  years. 
At  the  same  time  medicine  and  alchemy  were  also  cultivated. 

Concerned  as  he  was  to  secure  the  greatest  possible  accuracy, 
Tycho  constructed  instruments  of  great  size;  for  example,  a 
wooden  quadrant  for  outdoor  use  with  a  brass  scale  of  some  ten 
feet  radius,  permitting  readings  to  fractions  of  a  minute. 

The  best  artists  in  Augsburg,  clockmakers,  jewellers,  smiths,  and 
carpenters,  were  engaged  to  execute  the  work,  and  from  the  zeal 
which  so  noble  an  instrument  inspired,  the  quadrant  was  completed 
in  less  than  a  month.  Its  size  was  so  great  that  twenty  men  could 
with  difficulty  transport  it  to  its  place  of  fixture.  The  two  principal 
rectangular  radii  were  beams  of  oak;  the  arch  which  lay  between 
their  extremities  was  made  of  solid  wood  of  a  particular  kind,  and  the 
whole  was  bound  together  by  twelve  beams.  It  received  additional 
strength  from  several  iron  bands,  and  the  arch  was  covered  with 
plates  of  brass,  for  the  purpose  of  receiving  the  5400  divisions  into 
which  it  was  to  be  subdivided;  A  large  and  strong  pillar  of  oak,  shod 
with  iron,  was  driven  into  the  ground,  and  kept  in  its  place  by  solid 


URANIBORG. 


A  NEW  ASTRONOMY  207 

mason  work.  To  this  pillar  the  quadrant  was  fixed  in  a  vertical 
plane,  and  steps  were  prepared  to  elevate  the  observer,  when  stars  of 
a  low  altitude  required  his  attention.  As  the  instrument  could  not 
be  conveniently  covered  with  a  roof,  it  was  protected  from  the  weather 
by  a  covering  made  of  skins;  but  notwithstanding  this  and  other 
precautions,  it  was  broken  to  pieces  by  a  violent  storm,  after  having 
remained  uninjured  for  the  space  of  five  years.  —  Brewster. 

A  smaller  but  more  serviceable  azimuth  quadrant  of  brass  gave 
angles  to  the  nearest  minute.  He  had  a  copper  globe  constructed 
at  great  expense  with  the  positions  of  some  1000  stars  carefully 
marked  upon  it. 

The  very  precision  of  his  observations  tended  to  confirm  his 
scepticism  of  the  Copernican  hypothesis,  as  it  seemed  incredible 
that  the  earth's  supposed  orbital  motion  should  cause  no  change 
which  he  could  detect  in  the  position  and  brightness  of  the  stars. 
He  was  also  misled  by  supposing  that  the  stars  had  measurable 
angular  magnitude.  He  was  not  successful  in  making  any  funda- 
mental improvement  in  the  relatively  crude  methods  of  time 
measurement,  depending  himself  on  wheel-mechanism  without 
the  regulating  pendulum,  and  an  apparatus  of  the  sand-glass  or 
clepsydra  type. 

In  1577  Tycho  made  observations  on  a  brilliant  comet,  and 
drew  from  them  important  theoretical  inferences;  namely,  that 
instead  of  being  an  atmospheric  phenomenon,  the  comet  was  at 
least  three  times  as  remote  as  the  moon,  and  that  it  was  revolving 
about  the  sun  at  a  greater  distance  than  Venus  —  unimpeded  by 
the  familiar  crystalline  spheres.  He  was  even  led,  in  discussing 
apparent,  irregularities  of  its  motion,  to  suggest  that  its  orbit 
might  be  oval  —  foreshadowing  one  of  Kepler's  great  discoveries. 

According  to  the  current  view  of  his  time,  comets 

were  formed  by  the  ascending  from  the  earth  of  human  sins  and 
wickedness,  formed  into  a  kind  of  gas,  and  ignited  by  the  anger  of 
God.  This  poisonous  stuff  falls  down  again  on  people's  heads,  and 
causes  all  kinds  of  mischief,  such  as  pestilence,  Frenchmen  ( !),  sudden 
death,  bad  weather,  etc.  —  Dreyer,  Tycho  Brahe. 


208  A  SHORT  HISTORY  OF  SCIENCE 

Eleven  years  later  Tycho  published  a  volume  on  the  comet  as 
a  part  of  a  comprehensive  astronomical  treatise  which  was,  how- 
ever, never  completed.  About  the  same  time  his  royal  patron 
died,  and  the  new  administration  proved  less  sympathetic  with 
the  great  astronomer's  work  and  less  indulgent  with  his  extrava- 
gance and  personal  eccentricities. 

After  a  series  of  disagreements,  Tycho  withdrew  from  his  ob- 
servatory in  1597,  spent  the  winter  in  Hamburg,  and  after  nego- 
tiations with  different  sovereigns,  accepted  the  invitation  of  the 
Emperor  Rudolph  to  settle  in  Prague  in  1599.  Here  he  again 
organized  a  staff  of  assistants,  including,  to  the  great  advantage 
of  himself  and  of  his  science,  the  young  Kepler,  but  his  further 
progress  was  prematurely  terminated  by  death  in  1601,  at  the  age 
of  55. 

Tycho's  chief  services  to  the  progress  of  astronomy  consisted 
first,  in  the  superior  accuracy  of  his  instruments  and  observations, 
heightened  by  repetition  and  systematic  correction  of  errors; 
second,  in  the  extension  of  these  observations  over  a  long  series  of 
years.  In  both  respects  he  departed  from  current  practice,  and 
anticipated  the  modern.  In  point  of  accuracy  his  errors  of  star- 
places  seem  rarely  to  have  exceeded  1'  to  2',  and  he  even  de- 
termined the  length  of  the  year  within  one  second.  While  he 
recomputed  almost  every  important  astronomical  constant,  he 
accepted  the  traditional  distance  of  the  sun. 

Kepler  gave  striking  evidence  later  of  his  confidence  in  Tycho's 
accuracy  by  writing :  — 


'  Since  the  divine  goodness  has  given  to  us  in  Tycho  Brahe  a  most 
careful  observer,  from  whose  observations  the  error  of  8'  is  shewn  in 
this  calculation,  ...  it  is  right  that  we  should  with  gratitude  recog- 
nize and  make  use  of  this  gift  of  God.  .  .  .  For  if  I  could  have 
treated  8'  of  longitude  as  negligible  I  should  have  already  corrected 
sufficiently  the  hypothesis  .  .  .  discovered  in  chapter  xvi.  But  as 
they  could  not  be  neglected,  these  8'  alone  have  led  the  way  towards 
the  complete  reformation  of  astronomy,  and  have  made  the  subject- 
matter  of  a  great  part  of  this  work/  —  Berry. 


A  NEW  ASTRONOMY  209 


On  the  other  hand,  Tycho  was  not  strong  on  the  theoretical  side. 
He  was  never  willing  to  accept  the  Copernican  hypothesis  of 
rotation  and  orbital  motion  of  the  earth  —  maintaining,  for  ex- 
ample, that  if  the  earth  moved,  a  stone  dropped  from  the  top  of  a 
tower  must  fall  at  a  distance  from  the  foot.  Again  with  refer- 
ence to  the  apparent  displacement  of  the  stars  which  would  be 
expected  to  result  from  orbital  motion  of  the  earth,  he  says :  — 

A  yearly  motion  would  relegate  the  sphere  of  the  fixed  stars  to 
such  a  distance  that  the  path  described  by  the  earth  must  be  insig- 
nificant in  comparison.  Dost  thou  hold  it  possible  that  the  space 
between  the  sun,  the  alleged  centre  of  the  universe,  and  Saturn 
amounts  to  not  even  -^  of  that  distance  ?  At  the  same  time  this 
space  must  be  void  of  stars. 

Sensible,  however,  of  the  weakness  of  the  Ptolemaic  theory,  he 
devised  an  ingenious  compromise  in  which  the  planets  revolved 
about  the  Sun  in  their  respective  periods,  and  the  entire  heavens 
about  the  earth  daily  —  all  of  which  is  not  mathematically  dif- 
ferent from  the  Copernican  theory. 

We  see  in  him  at  the  same  time  a  perfect  son  of  the  sixteenth 
century,  believing  the  universe  to  be  woven  together  by  mysterious 
connecting  threads  which  the  contemplation  of  the  stars  or  of  the 
elements  of  nature  might  unravel,  and  thereby  lift  the  veil  of  the 
future;  we  see  that  he  is  still,  like  most  of  his  contemporaries,  a 
believer  in  the  solid  spheres  and  the  atmospherical  origin  of  comets, 
to  which  errors  of  the  Aristotelean  physics  he  was  destined  a  few 
years  later  to  give  the  death-blow  by  his  researches  on  comets; 
we  see  him  also  thoroughly  discontented  with  his  surroundings,  and 
looking  abroad  in  the  hope  of  finding  somewhere  else  the  place  and 
the  means  for  carrying  out  his  plans. 

As  a  practical  astronomer  Tycho  has  not  been  surpassed  by  any 
observer  of  ancient  or  modern  times.  The  splendor  and  number  of 
his  instruments,  the  ingenuity  which  he  exhibited  in  inventing  new  ones 
and  in  improving  and  adding  to  those  which  were  formerly  known, 
and  his  skill  and  assiduity  as  an  observer,  have  given  a  character  to 
his  labors  and  a  value  to  his  observations  which  will  be  appreciated 
to  the  latest  posterity.  —  Brewster. 


210  A  SHORT  HISTORY  OF  SCIENCE 

KEPLER.  —  Pierre  de  la  Ramee,  or  Petrus  Ramus,  a  French 
mathematician  and  philosopher,  impatient  with  the  cumbrous 
astronomical  hypotheses  of  the  ancients,  and  unsatisfied  with 
Copernicus'  proposed  simplification,  published  a  work  in  1569 
expressing  the  hope 

'  that  some  distinguished  German  philosopher  would  arise  and  found 
a  new  astronomy  on  careful  observations  by  means  of  logic  and  mathe- 
matics, discarding  all  the  notions  of  the  ancients/ 

Within  a  few  months  he  discussed  the  matter  at  length  with 
Tycho  Brahe  at  Augsburg.  Without  accepting  Ramus'  views, 
the  young  astronomer  did  make  it  his  life  work  to  lay  the  neces- 
sary foundation  for  such  a  new  astronomy.  Thirty  years  later, 
Mastlin,  professor  at  Tubingen,  wrote  his  former  student  Kepler 
—  then  aged  28  — 

that  Tycho  'had  hardly  left  a  shadow  of  what  had  hitherto  been 
taken  for  astronomical  science,  and  that  only  one  thing  was  certain, 
which  was  that  mankind  knew  nothing  of  astronomical  matters/ 

Born  late  in  1571  in  Wiirtemberg,  of  Protestant  parents  in 
very  straitened  circumstances,  Johann  Kepler's  whole  life  was  a 
struggle  against  poverty,  ill-health,  and  adverse  conditions.  In 
1594,  abandoning  with  some  hesitation  theological  studies,  for 
which  his  acceptance  of  the  new  Copernican  hypothesis  dis- 
qualified him,  he  was  appointed  lecturer  on  mathematics  at  Gratz. 
Students  were  few,  and  his  duties  included  the  preparation  of  a 
yearly  almanac,  containing,  besides  what  its  name  implies,  a 
variety  of  weather  predictions  and  astrological  information. 
"Mother  Astronomy,"  he  says,  "would  surely  have  to  suffer 
hunger  if  the  daughter  Astrology  did  not  earn  their  bread." 

Becoming  thus  more  interested  in  astronomy,  "there  were,"  he 
says,  "  three  things  in  particular :  viz.,  the  number,  the  size,  and 
the  motion  of  the  heavenly  bodies,  as  to  which  I  searched  zealously 
for  reasons  why  they  were  as  they  were  and  not  otherwise."  The 
first  result  which  seemed  to  him  important,  though  somewhat 
fantastic  from  our  standpoint,  was  a  crude  correspondence  be- 


KEPLER  (Opera  omnia). 


A  NEW  ASTRONOMY  211 

tween  the  planetary  orbits  and  the  five  regular  solids,  published 
in  1596  under  a  title  which  may  be  abridged  to  Cosmographic 
Mystery. 

The  Earth  is  the  circle,  the  measure  of  all.  Round  it  describe  a 
dodecahedron,  the  circle  including  this  will  be  Mars.  Round  Mars  de- 
scribe a  tetrahedron,  the  circle  including  this  will  be  Jupiter.  De- 
scribe a  cube  round  Jupiter,  the  circle  including  this  will  be  Saturn. 
Then  inscribe  in  the  Earth  an  icosahedron,  the  circle  inscribed  in  it 
will  be  Venus.  Inscribe  an  octahedron  in  Venus,  the  circle  inscribed 
in  it  will  be  Mercury. 

Kepler  declared  that  he  would  not  renounce  the  glory  of  this 
discovery  "for  the  whole  Electorate  of  Saxony."  The  corre- 
spondence of  the  dimensions  of  this  fantastic  geometrical  con- 
struction with  the  distances  of  members  of  our  solar  system  is 
in  reality  far  from  close,  but  both  Tycho  Brahe  and  Galileo 
seem  to  have  been  favorably  impressed  by  the  book. 

The  difficulties  of  Kepler's  position  as  a  Protestant  in  Gratz 
led  him,  after  a  preliminary  visit,  to  accept  an  engagement  as 
Tycho' s  assistant  at  Prague. 

The  powers  of  original  genius  were  then  for  the  first  time  as- 
sociated with  inventive  skill  and  patient  observation,  and  though  the 
astronomical  data  provided  by  Tycho  were  sure  of  finding  their  ap- 
plication in  some  future  age,  yet  without  them,  Kepler's  speculations 
would  have  been  vain  and  the  laws  which  they  enabled  him  to  deter- 
mine would  have  adorned  the  history  of  another  century.  —  Brewster. 

In  1602  Kepler  succeeded  Tycho  as  imperial  mathematician. 
Most  fortunately,  also,  he  secured  possession  of  his  chief's  great 
collection  of  observations,  though  not  of  the  instruments,  —  a 
matter  of  less  consequence,  since  Kepler  like  Copernicus  was  a 
mathematician  rather  than  an  observer.  To  the  study  of  these 
records  he  devoted  the  next  25  years.  Among  all  the  planetary 
observations  of  Tycho  Brahe  those  of  Mars  presented  the  irregu- 
larities most  difficult  of  explanation,  and  it  was  these  which,  having 
been  originally  assigned  to  Kepler,  engrossed  his  attention  for 
many  years,  and  in  the  end  led  to  some  of  his  finest  discoveries. 


212  A  SHORT  HISTORY  OF  SCIENCE 

The  Copernican  theory  like  the  Ptolemaic  involved  the  resolu- 
tion of  the  motion  of  each  planet  into  a  main  circular  motion, 
modified  by  superimposing  other  circular  motions  —  epicycles  — 
successively  upon  it,  each  circle  being  the  path  of  the  centre  of  the 
next.  Even  after  disentangling  the  essential  irregularities  of 
Mars'  orbit  from  those  merely  due  to  irregular  motion  of  the  earth, 
he  could  still  obtain  no  satisfactory  agreement  with  Tycho's 
records,  of  which,  as  has  been  said,  he  refused  to  doubt  the  ac- 
curacy. Taking  advantage  of  his  own  failure  —  as  happens  to 
men  of  true  genius  —  he  abandoned  the  restriction  of  circular 
motions,  and  experimented  with  other  closed  curves,  of  which 
the  ellipse  is  simplest.  Taking  the  sun  at  a  focus,  the  problem 
was  at  last  solved,  theory  and  observation  reconciled  within  due 
limits  of  error.  At  the  same  time  uniform  motion  was  naturally 
abandoned,  for  with  a  non-circular  orbit,  it  was  evident  that  the 
planet  could  not  describe  both  equal  distances  and  equal  areas 
in  equal  times.  Here,  again,  Kepler's  scientific  imagination  led 
him  to  the  great  discovery  that  the  planet  traverses  its  orbit  in 
such  a  manner  that  a  line  joining  it  to  the  sun  would  describe 
sectors  of  equal  area  in  equal  times,  the  planet  thus  moving 
fastest  when  nearest  the  sun. 

Of  Kepler's  celebrated  three  laws,  the  first  two  are: 

The  planet  describes  an  ellipse,  the  sun  being  in  one  focus. 

The  straight  line  joining  the  planet  to  the  sun  sweeps  out 
equal  areas  in  equal  intervals  of  time. 

These  results  were  published  in  1609  as  part  of  extended  Com- 
mentaries on  the  Motions  of  Mars. 

The  great  problem  was  solved  at  last,  the  problem  which  had 
baffled  the  genius  of  Eudoxus  and  had  been  a  stumbling-block  to  the 
Alexandrian  astronomers,  to  such  an  extent  that  Pliny  had  called 
Mars  the  inobservabile  sidus.  The  numerous  observations  made 
by  Tycho  Brahe,  with  a  degree  of  accuracy  never  before  attained, 
had  in  the  skilful  hand  of  Kepler  revealed  the  unexpected  fact  that 
Mars  describes  an  ellipse,  in  one  of  the  foci  of  which  the  sun  is  situated, 
and  that  the  radius  vector  of  the  planet  sweeps  over  equal  areas  in 
equal  times.  And  the  genius  and  astounding  patience  of  Kepler  had 


A  NEW  ASTRONOMY  213 

proved  that  not  only  did  this  new  theory  satisfy  the  observations, 
but  that  no  other  hypothesis  could  be  made  to  agree  with  the  obser- 
vations, as  every  proposed  alternative  left  outstanding  errors,  such 
as  it  was  impossible  to  ascribe  to  errors  of  observation.  Kepler  had 
therefore,  unlike  all  his  predecessors,  not  merely  put  forward  a  new 
hypothesis  which  might  do  as  well  as  another  to  enable  a  computer 
to  construct  tables  of  the  planet's  motion;  he  had  found  the  actual 
orbit  in  which  the  planet  travels  through  space. 

In  the  history  of  astronomy  there  are  only  two  other  works  of 
equal  importance,  the  book  De  Revolutionibus  of  Copernicus  and 
the  Principia  of  Newton.  The  'astronomy  without  hypothesis' 
demanded  by  Ramus  had  at  last  been  produced,  and  well  might 
Kepler  proclaim : 

'  It  is  well,  Ramus,  that  you  have  run  from  this  pledge,  by  quitting 
life  and  your  professorship ;  if  you  held  it  still,  I  should,  with  justice, 
claim  it.' 

Resuming  later  the  tendency  of  his  Cosmographic  Mystery, 
he  published  in  1619  his  Harmony  of  the  World,  containing  his 
third  law :  — 

The  squares  of  the  times  of  revolution  of  any  two  planets  (in- 
cluding the  earth)  about  the  sun  are  proportional  to  the  cubes  of 
their  mean  distances  from  the  sun. 

In  his  delight  he  exclaims  'Nothing  holds  me,  I  will  indulge  in 
my  sacred  fury ;  I  will  triumph  over  mankind  by  the  honest  confession 
that  I  have  stolen  the  golden  vases  of  the  Egyptians  to  build  up  a 
tabernacle  for  my  God,  far  away  from  the  confines  of  Egypt/  — 

'  What  sixteen  years  ago,  I  urged  as  a  thing  to  be  sought,  that  for 
which  I  joined  Tycho  Brahe,  for  which  I  settled  in  Prague,  for  which 
I  have  devoted  the  best  part  of  my  life  to  astronomical  contempla- 
tions —  at  length  I  have  brought  to  light,  and  recognized  its  truth 
beyond  my  most  sanguine  expectations.  It  is  not  eighteen  months 
since  I  got  the  first  glimpse  of  light,  three  months  since  the  dawn, 
very  few  days  since  the  unveiled  sun,  most  admirable  to  gaze  on, 
burst  out  upon  me.'  .  .  . 

Archimedes  of  old  had  said  "  Give  me  a  place  to  stand  on,  and 
I  shall  move  the  world."  Tycho  Brahe  had  given  Kepler  the 
place  to  stand  on,  a.nd  Kepler  did  move  the  world. 


214  A  SHORT  HISTORY  OF  SCIENCE 

It  should  be  borne  in  mind  that  Kepler's  results  depend  not 
on  a  priori  theory  for  their  confirmation,  but  upon  actual  ob- 
servations supporting  them  and  interpreted  by  them.  The  great 
further  step  of  showing  that  the  three  laws  are  not  independent 
and  empirical,  but  mathematical  consequences  of  a  single  me- 
chanical law  still  awaited  the  genius  of  Newton. 

Kepler's  notions  in  regard  to  force  and  motion  are  still  crude. 
Thus,  for  example,  having  in  mind  an  analogy  with  magnetism, 
Kepler  says  in  his  Epitome  of  the  Copernican  Astronomy, 
(1618-1621):  — 

'There  is  therefore  a  conflict  between  the  carrying  power  of  the 
sun  and  the  impotence  or  material  sluggishness  (inertia)  of  the  planet ; 
each  enjoys  some  measure  of  victory,  for  the  former  moves  the  planet 
from  its  position  and  the  latter  frees  the  planet's  body  to  some  extent 
from  the  bonds  in  which  it  is  thus  held  .  .  .  but  only  to  be  captured 
again  by  another  portion  of  this  rotatory  virtue.' 

Elsewhere  he  says :  — 

1  We  must  suppose  one  of  two  things  :  either  that  the  moving  spirits, 
in  proportion  as  they  are  more  removed  from  the  sun,  are  more  feeble ; 
or  that  there  is  one  moving  spirit  in  the  centre  of  all  the  orbits, 
namely,  in  the  sun,  which  urges  each  body  the  more  vehemently  in 
proportion  as  it  is  nearer;  but  in  more  distant  spaces  languishes  in 
consequence  of  the  remoteness  and  attenuation  of  its  virtue.' 

—  Whewell. 

He  recognized  the  necessity  of  a  force  exercised  by  the  sun,  but 
believed  it  inversely  proportional  to  the  distance  instead  of  to 
the  square  of  the  distance.  His  notions  of  gravity  are  expressed 
in  his  book  on  Mars:  — 

'  Every  bodily  substance  will  rest  in  any  place  in  which  it  is  placed 
isolated,  outside  the  reach  of  the  power  of  a  body  of  the  same  kind. 
Gravity  is  the  mutual  tendency  of  cognate  bodies  to  join  each  other 
(of  which  kind  the  magnetic  force  is),  so  that  the  earth  draws  a  stone 
much  more  than  the  stone  draws  the  earth.  Supposing  that  the 
earth  were  in  the  centre  of  the  world,  heavy  bodies  would  not  seek 
the  centre  of  the  world  as  such,  but  the  centre  of  a  round,  cognate 


A  NEW  ASTRONOMY  215 

body,  the  earth ;  and  wherever  the  earth  is  transported  heavy  bodies 
will  always  seek  it ;  but  if  the  earth  were  not  round  they  would  not 
from  all  sides  seek  the  middle  of  it,  but  would  from  different  sides  be 
carried  to  different  points.  If  two  stones  were  situated  anywhere  in 
space  near  each  other,  but  outside  the  reach  of  a  third  cognate  body, 
they  would  after  the  manner  of  two  magnetic  bodies  come  together 
at  an  intermediate  point,  each  approaching  the  other  in  proportion 
to  the  attracting  mass.  And  if  the  earth  and  the  moon  were  not  kept 
in  their  orbits  by  their  animal  force,  the  earth  would  ascend  towards 
the  moon  one  fifty-fourth  part  of  the  distance,  while  the  moon  would 
descend  the  rest  of  the  way  and  join  the  earth,  provided  that  the  two 
bodies  are  of  the  same  density.  If  the  earth  ceased  to  attract  the 
water  all  the  seas  would  rise  and  flow  over  the  moon.  —  Dreyer. 

Kepler's  last  important  published  work  was  his  Rudolphine 
Tables  (1627),  embodying  the  accumulated  results  of  Tycho's 
work  and  his  own,  and  remaining  a  standard  for  a  century.  It  is 
noteworthy  that  during  Kepler's  work  on  these  tables,  mathe- 
matical computation  was  peacefully  revolutionized  by  the  intro- 
duction of  logarithms,  newly  discovered  by  Napier  and  Biirgi. 

In  1628,  after  vain  attempts  to  collect  arrears  of  his  salary  as 
imperial  mathematician,  he  even  joined  Wallenstein  as  astrologer, 
but  died  soon  after  at  Regensburg  in  1630. 

Kepler  also  wrote  an  important  work  on  Dioptrics  with  a  mathe- 
matical discussion  of  refraction  and  the  different  forms  of  the 
newly  invented  telescope,  the  whole  constituting  the  foundation 
of  modern  optics.  In  it  he  develops  the  first  correct  theory  of 
vision,  "Seeing  amounts  to  feeling  the  stimulation  of  the  retina, 
which  is  painted  with  the  colored  rays  of  the  visible  world.  The 
picture  must  then  be  transmitted  to  the  brain  by  a  mental  cur- 
rent, and  delivered  at  the  seat  of  the  visual  faculty."  He  sup- 
poses that  color  depends  on  density  and  transparency,  and  that 
refraction  is  due  to  greater  resistance  of  a  dense  medium.  He 
enunciates  the  law  that  intensity  of  light  varies  inversely  as  the 
square  of  the  distance.  "  In  proportion  as  the  spherical  surface 
from  whose  'centre  the  light  proceeds  is  greater  or  smaller,  so  is 
the  strength  or  density  of  the  light-rays  which  fall  on  the  smaller 


216  A  SHOUT  HISTORY  OF  SCIENCE 

sphere  to  the  strength  of  those  rays  which  fall  on  the  larger 
sphere."  He  explains  the  estimation  of  distance  by  binocular 
vision.  He  supposes  the  velocity  of  light  to  be  infinite.  His 
more  purely  mathematical  work  will  be  mentioned  in  a  later 
chapter. 

Kepler  added  Plato's  boldness  of  fancy  to  his  own  patient  and 
candid  habit  of  testing  his  fancies  by  a  rigorous  and  laborious  com- 
parison with  the  phenomena ;  and  thus  his  discoveries  led  to  those  of 
Newton.  —  Whewell. 

If  Kepler  had  burnt  three-quarters  of  what  he  printed,  we  should 
in  all  probability  have  formed  a  higher  opinion  of  his  intellectual 
grasp  and  sobriety  of  judgment,  but  we  should  have  lost  to  a  great 
extent  the  impression  of  extraordinary  enthusiasm  and  industry,  and 
of  almost  unequalled  intellectual  honesty,  which  we  now  get  from  a 
study  of  his  works. —  Berry. 

Kepler  says:  'If  Christopher  Columbus,  if  Magellan,  if  the 
Portuguese,  when  they  narrate  their  wanderings,  are  not  only  ex- 
cused, but  if  we  do  not  wish  these  passages  omitted,  and  should  lose 
much  pleasure  if  they  were,  let  no  one  blame  me  for  doing  the  same/ 
Kepler's  talents  were  a  kindly  and  fertile  soil,  which  he  cultivated 
with  abundant  toil  and  vigor,  but  with  great  scantiness  of  agricultural 
skill  and  implements.  Weeds  and  the  grain  throve  and  flourished 
side  by  side  almost  undistinguished;  and  he  gave  a  peculiar  appear- 
ance to  his  harvest,  by  gathering  and  preserving  the  one  class  of  plants 
with  as  much  care  and  diligence  as  the  other.  —  Whewell. 

Endowed  with  two  qualities,  which  seemed  incompatible  with 
each  other,  a  volcanic  imagination  and  a  pertinacity  of  intellect  which 
the  most  tedious  numerical  calculations  could  not  daunt,  Kepler 
conjectured  that  the  movements  of  the  celestial  bodies  must  be  con- 
nected together  by  simple  laws,  or,  to  use  his  own  expression,  by 
harmonic  laws.  These  laws  he  undertook  to  discover.  A  thousand 
fruitless  attempts,  errors  of  calculation  inseparable  from  a  colossal 
undertaking,  did  not  prevent  him  a  single  instant  from  advancing 
resolutely  toward  the  goal  of  which  he  imagined  he  had  obtained  a 
glimpse.  Twenty-two  years  were  employed  by  him  in  this  investiga- 
tion, and  still  he  was  not  weary  of  it !  What,  in  reality,  are  twenty- 
two  years  of  labor  to  him  who  is  about  to  become  the  legislator  of 
worlds;  who  shall  inscribe  his  name  in  ineffaceable  characters  upon 


QALILEVS  G A 

-  /    ANNVM  AGENS  ocxv- 


GALILEO  (Opere,  1744). 


A  NEW  ASTRONOMY  217 

the  frontispiece  of  an  immortal  code;  who  shall  be  able  to  exclaim 
in  dithyrambic  language,  and  without  incurring  the  reproach  of  any- . 
one,  '  The  die  is  cast ;  I  have  written  my  book ;  it  will  be  read  either 
in  the  present  age  or  by  posterity,  it  matters  not  which ;  it  may  well 
await  a  reader,  since  God  has  waited  six  thousand  years  for  an  inter- 
preter of  his  words/  —  Arago. 

The  philosophical  significance  of  Kepler's  discoveries  was  not 
recognized  by  the  ecclesiastical  party  at  first.  It  is  chiefly  this,  that 
they  constitute  a  most  important  step  to  the  establishment  of  the 
doctrine  of  the  government  of  the  world  by  law.  But  it  was  im- 
possible to  receive  these  laws  without  seeking  for  their  cause.  The 
result  to  which  that  search  eventually  conducted  not  only  explained 
their  origin,  but  also  showed  that,  as  laws,  they  must,  in  the  necessity 
of  nature,  exist.  It  may  be  truly  said  that  the  mathematical  exposi- 
tion of  their  origin  constitutes  the  most  splendid  monument  of  the 
intellectual  power  of  man.  —  Draper. 

GALILEO.  —  Columbus  discovered  America  when  Copernicus 
was  but  19,  and  before  the  birth  of  Tycho  Brahe,  Magellan  had 
completed  the  proof  of  the  earth's  rotundity  by  actually 
sailing  around  it,  while  Luther  had  stirred  up  the  great  religious 
revolt  of  Protestantism.  The  later  years  of  Kepler  and  Galileo 
fell  within  the  period  of  the  Thirty  Years'  War,  of  which  neither 
was  to  witness  the  close.  Permanent  English  settlements  in 
America  had  just  begun.  Galileo  (1564-1642),  born  on  the  day 
of  Michael  Angelo's  death,  "  nature  seeming  to  signify  thereby  the 
passing  of  the  sceptre  from  art  to  science, "  and  in  the  same  year 
with  Shakespeare,  exerted  a  mighty  influence  on  the  development 
of  science  in  many  fields,  and  in  particular  laid  the  foundations 
of  modern  dynamics. 

It  is  a  remarkable  circumstance  in  the  history  of  science  that 
astronomy  should  have  been  cultivated  at  the  same  time  by  three  such 
distinguished  men  as  Tycho,  Kepler  and  Galileo.  While  Tycho  in 
the  54th  year  of  his  age  was  observing  the  heavens  at  Prague,  Kepler, 
only  30  years  old,  was  applying  his  wild  genius  to  the  determination 
of  the  orbit  of  Mars,  and  Galileo,  at  the  age  of  36,  was  about  to  direct 
the  telescope  to  the  unexplored  regions  of  space.  The  diversity  of 
gifts  which  Providence  assigned  to  these  three  philosophers  was  no 


218  A  SHORT  HISTORY  OF  SCIENCE 

less  remarkable.  Tycho  was  destined  to  lay  the  foundation  of  modern 
astronomy  by  a  vast  series  of  accurate  observations  made  with  the 
largest  and  the  finest  instruments;  it  was  the  proud  lot  of  Kepler  to 
deduce  the  laws  of  the  planetary  orbits  from  the  observations  of  his 
predecessors;  while  Galileo  enjoyed  the  more  dazzling  honor  of 
discovering  by  the  telescope  new  celestial  bodies  and  new  systems 
of  worlds.  —  Brewster. 

Coming  into  a  world  still  dominated  by  the  Aristotelian  tradi- 
tion, Galileo  is  puzzled  by  the  conflict  between  his  own  obser- 
vations and  the  accepted  theories,  but  firm  and  fearless  in  his 
convictions,  he  eagerly  and  powerfully  controverts  the  older  notions, 
incidentally  gaining  enemies  as  well  as  disciples.  What  those 
accepted  theories  were  may  be  exemplified  by  the  following  pas- 
sages from  a  work  of  Daniel  Schwenter  (1585-1636),  professor  of 
mathematics  at  Altdorf : — 

'When  a  body  falls  it  moves  faster  the  nearer  it  approaches  the 
earth.  The  farther  it  falls  the  more  power  it  possesses.  For  every- 
thing which  is  heavy,  hastens  according  to  the  opinion  of  philosophers 
towards  its  natural  place,  that  is  the  centre  of  the  earth,  just  as  man 
returning  to  his  fatherland  becomes  the  more  eager  the  nearer  he 
comes,  and  therefore  hastens  so  much  the  more.  Still  another  natural 
cause  contributes  to  this.  The  air  which  is  parted  by  the  falling  ball, 
hastens  together  again  behind  the  ball  and  drives  it  always  harder.7 

If  the  Copernican  theory  were  true,  the  bullet  remaining  two 
minutes  in  the  air  would  be  left  many  miles  behind  by  the  revolv- 
ing earth,  —  a  distance  which  the  moving  atmosphere  could  not 
possibly  carry  it.  The  rainbow  is  "a  mirror  in  which  the  human 
understanding  can  behold  its  ignorance  in  broad  day."  The 
powder  drives  the  bullet  in  an  oblique  line  to  the  highest  point 
of  its  path,  then  follows  motion  in  an  arc,  finally,  the  natural 
motion  vertically  downward. 

In  his  whole  point  of  view  and  habit  of  mind  Galileo  embodied 
the  attitude  and  spirit  of  modern  science.  He  was  keenly  alert 
in  observing,  analyzing,  and  reflecting  on  natural  phenomena, 
eager  and  convincing  in  his  expositions,  sceptical  and  intolerant 


A  NEW  ASTRONOMY  219 

of  mere  authority,  whether  in  science,  philosophy,  or  theology. 
It  was  a  true  instinct  of  the  conservatives  to  recognize  in  him 
the  champion  of  a  principle  fatally  hostile  to  their  own.  Between 
these  antagonistic  principles  no  permanent  peace  was  possible. 

While  still  a  mere  youth,  he  discovered  the  regularity  of  pendulum 
vibrations  by  observing  the  slow  swinging  of  the  cathedral  lamp 
of  Pisa  (1582).  Before  he  was  25  he  published  work  on  the 
hydrostatic  balance  (1586),  and  on  the  centre  of  gravity  of  solids. 
Only  a  little  later  he  conducted  at  the  leaning  tower  simple  ex- 
periments in  falling  bodies,  which  upset  world-old  notions  on 
this  everyday  matter,  showing  that  the  velocity  of  descent  is 
not,  as  was  commonly  supposed,  proportional  to  weight.  And 
"yet  the  Aristotelians,  who  with  their  own  eyes  saw  the  unequal 
weights  strike  the  ground  at  the  same  instant,  ascribed  the  effect 
to  some  unknown  cause,  and  preferred  the  decision  of  their  master 
to  that  of  nature  herself." 

He  further  showed  that  the  hypothesis  of  uniform  acceleration 
accounted  correctly  for  the  observed  relations  between  space, 
time  and  velocity,  and  that  the  path  of  a  projectile  is  a  parabola. 
In  the  words  of  a  recent  authority,  when  Galileo 

deduced  by  experiment,  and  described  with  mathematical  pre- 
cision, the  acceleration  of  a  falling  body,  he  probably  contributed 
more  to  the  physical  sciences  than  all  the  philosophers  who  had 
preceded  him. 

Hearing  of  the  telescope  newly  invented  in  Holland,  he  con- 
structed one  for  himself,  by  means  of  which  he  discovered  sun 
spots,  the  mountains  of  the  moon,  the  satellites  of  Jupiter,  the 
rings  of  Saturn,  and  the  phases  of  Venus.  The  sensation  created 
by  these  discoveries  is  described  in  the  following  passages  from 
Fahie's  Life  of  Galileo  and  Brewster's  Martyrs  of  Science. 

'As  the  news  had  reached  Venice  that  I  had  made  such  an  in- 
strument, six  days  ago  I  was  summoned  before  their  Highnesses,  the 
Signoria,  and  exhibited  it  to  them,  to  the  astonishment  of  the  whole 
senate.  Many  of  the  nobles  and  senators,  although  of  a  great  age, 
mounted  more  than  once  to  the  top  of  the  highest  church  tower  in 


220  A  SHORT  HISTORY  OF  SCIENCE 

Venice,  in  order  to  see  sails  and  shipping  that  were  so  far  off  that  it 
was  two  hours  before  they  were  seen,  without  my  spy-glass,  steering 
full  sail  into  the  harbour ;  for  the  effect  of  my  instrument  is  such  that 
it  makes  an  object  50  miles  off  appear  as  large  as  if  it  were  only 
five/ 

'  But  the  greatest  marvel  of  all  is  the  discovery  of  four  new  planets. 
I  have  observed  their  motions  proper  to  themselves  and  in  relation 
to  each  other,  and  wherein  they  differ  from  the  motions  of  the  other 
planets.  These  new  bodies  move  round  another  very  great  star,  in 
the  same  way  as  Mercury  and  Venus,  and,  peradventure,  the  other 
known  planets,  move  round  the  sun.  As  soon  as  my  tract  is  printed, 
which  I  intend  sending  as  an  advertisement  to  all  philosophers  and 
mathematicians,  I  shall  send  a  copy  to  his  Highness,  the  Grand  Duke, 
together  with  an  excellent  spy-glass,  which  will  enable  him  to  judge 
for  himself  of  the  truth  of  these  novelties/  —  Fahie. 

Galileo's  discoveries  on  the  surface  of  the  moon  were  ill  received 
by  the  followers  of  Aristotle.  According  to  their  preconceived  opin- 
ions, the  moon  was  perfectly  spherical  and  absolutely  smooth ;  and  to 
cover  it  with  mountains  and  scoop  it  out  into  valleys  was  an  act  of 
impiety  which  defaced  the  regular  forms  which  Nature  herself  had 
imprinted.  It  was  in  vain  that  Galileo  appealed  to  the  evidence 
of  observation  and  to  the  actual  surface  of  our  own  globe.  The  very 
irregularities  on  the  moon  were,  in  his  opinion,  a  proof  of  divine  wisdom ; 
and  had  its  surface  been  absolutely  smooth,  it  would  have  been  '  but 
a  vast  unblessed  desert,  void  of  animals,  of  plants,  of  cities,  and  men 
—  the  abode  of  silence  and  inaction  —  senseless,  lifeless,  soulless,  and 
stripped  of  all  those  ornaments  which  now  render  it  so  varied  and  so 
beautiful/ 

In  examining  the  fixed  stars  and  comparing  them  with  the  planets, 
Galileo  observed  a  remarkable  difference  in  the  appearance  of  their 
discs.  All  the  planets  appeared  with  round  globular  discs  like  the 
moon;  whereas  the  fixed  stars  never  exhibited  any  disc  at  all  but 
resembled  lucid  points  sending  forth  twinkling  rays.  Stars  of  all 
magnitudes  he  found  to  have  the  same  appearance;  those  of  the 
fifth  and  sixth  magnitude  having  the  same  character,  when  seen 
through  a  telescope,  as  Sirius,  the  largest  of  the  stars,  when  seen  by 
the  naked  eye. 

Important  and  interesting  as  these  discoveries  were,  they  were 
thrown  into  the  shade  by  those  to  which  he  was  led  during  a  careful 


A  NEW  ASTRONOMY  221 

examination  of  the  planets  with  a  more  powerful  telescope.  On  the 
7th  of  January,  1610,  at  one  o'clock  in  the  morning,  when  he  directed 
his  telescope  to  Jupiter,  he  observed  three  stars  near  the  body  of  the 
planet,  two  being  to  the  east  and  one  to  the  west  of  him.  They  were 
all  in  a  straight  line,  and  parallel  to  the  ecliptic  and  appeared  brighter 
than  other  stars  of  the  same  magnitude.  Believing  them  to  be  fixed 
stars,  he  paid  no  great  attention  to  their  distances  from  Jupiter  and 
from  one  another.  On  the  8th  of  January,  however,  when,  from  some 
cause  or  other,  he  had  been  led  to  observe  the  stars  again,  he  found  a 
very  different  arrangement  of  them;  all  the  three  were  on  the  west 
side  of  Jupiter,  nearer  one  another  than  before  and  almost  at  equal 
distances.  Though  he  had  not  turned  his  attention  to  the  extraordi- 
nary fact  of  the  mutual  approach  of  the  stars,  yet  he  began  to  con- 
sider how  Jupiter  could  be  found  to  the  east  of  the  three  stars,  when 
but  the  day  before  he  had  been  to  the  west  of  two  of  them.  The  only 
explanation  which  he  could  give  of  this  fact  was  that  the  motion  of 
Jupiter  was  direct,  contrary  to  the  astronomical  calculations  and 
that  he  had  got  before  these  two  stars  by  his  own  motion. 

In  this  dilemma  between  the  testimony  of  his  senses  and  the  results 
of  calculation,  he  waited  for  the  following  night  with  the  utmost 
anxiety,  but  his  hopes  were  disappointed,  for  the  heavens  were  wholly 
veiled  in  clouds.  On  the  10th,  two  only  of  the  stars  appeared,  and 
both  on  the  east  side  of  the  planet.  As  it  was  obviously  impossible 
that  Jupiter  could  have  advanced  from  west  to  east  on  the  8th  of 
January,  and  from  east  to  west  on  the  10th,  Galileo  was  forced  to 
conclude  that  the  phenomenon  which  he  had  observed  arose  from  the 
motion  of  the  stars,  and  he  set  himself  to  observe  diligently  their  change 
of  place.  On  the  llth  there  were  still  only  two  stars,  and  both  to  the 
east  of  Jupiter,  but  the  more  eastern  star  was  now  twice  as  large  as 
the  other  one,  though  on  the  preceding  night  they  had  been  per- 
fectly equal.  This  fact  threw  a  new  light  upon  Galileo's  difficulties, 
and  he  immediately  drew  the  conclusion,  which  he  considered  to  be 
indubitable, '  that  there  were  in  the  heavens  three  stars  which  revolve 
around  Jupiter,  in  the  same  manner  as  Venus  and  Mercury  revolve 
around  the  sun.'  On  the  12th  of  January  he  again  observed  them  in 
new  positions,  and  of  different  magnitudes;  and  on  the  13th  he 
discovered  a  fourth  star,  which  completed  the  four  secondary  planets 
with  which  Jupiter  is  surrounded.  —  Brewster. 

His  results  were  published  in  '  The  Sidereal  Messenger/  announc- 


222  A  SHORT  HISTORY  OF  SCIENCE 

ing  'great  and  very  wonderful  spectacles,  and  offering  them  to  the 
consideration  of  every  one,  but  especially  of  philosophers  and  as- 
tronomers; which  have  been  observed  by  Galileo  Galilei  ...  by 
the  assistance  of  a  perspective  glass  lately  invented  by  him ;  namely 
in  the  face  of  the  moon,  in  innumerable  fixed  stars  in  the  Milky  Way, 
in  nebulous  stars,  but  especially  in  four  planets  which  revolve  around 
Jupiter  at  different  intervals  and  periods  with  a  wonderful  celerity; 
which,  hitherto  not  known  to  any  one,  the  author  has  recently  been 
the  first  to  detect,  and  has  decreed  to  call  the  Medicean  stars/ 

—  Whewell 

The  reception  which  these  discoveries  met  with  from  Kepler  is 
highly  interesting,  and  characteristic  of  the  genius  of  that  great  man. 
He  was  one  day  sitting  idle  and  thinking  of  Galileo,  when  his  friend 
Wachenfels  stopped  his  carriage  at  his  door  to  communicate  to  him 
some  intelligence.  'Such  a  fit  of  wonder/  says  he,  ' seized  me  at  a 
report  which  seemed  to  be  so  very  absurd,  and  I  was  thrown  into  such 
agitation  at  seeing  an  old  dispute  between  us  decided  in  this  way, 
that  between  his  joy,  my  coloring,  and  the  laughter  of  both,  confounded 
as  we  were  by  such  a  novelty,  we  were  hardly  capable,  he  of  speaking, 
or  I  of  listening.  On  our  parting,  I  immediately  began  to  think  how 
there  could  be  any  addition  to  the  number  of  the  planets  without 
overturning  my  Cosmographic  Mystery,  according  to  "which  Euclid's 
five  regular  solids  do  not  allow  more  than  six  planets  round  the  sun.  .  . 
I  am  so  far  from  disbelieving  the  existence  of  the  four  circumjovial 
planets,  that  I  long  for  a  telescope,  to  anticipate  you,  if  possible,  in 
discovering  two  round  Mars,  as  the  proportion  seems  to  require,  six 
or  eight  round  Saturn,  and  perhaps  one  each  round  Mercury  and 
Venus/ 

In  a  very  different  spirit  did  the  Aristotelians  receive  the  Sidereal 
Messenger  of  Galileo.  The  principal  professor  of  philosophy  at 
Padua  resisted  Galileo's  repeated  and  urgent  entreaties  to  look  at 
the  moon  and  planets  through  his  telescope ;  and  he  even  labored  to 
convince  the  Grand  Duke  that  the  satellites  of  Jupiter  could  not  pos- 
sibly exist.1 

'  There  are  seven  windows  given  to  animals  in  the  domicile  of  the 
head,  through  which  the  air  is  admitted  to  the  tabernacle  of  the  body, 

1 '  As  I  wished  to  show  the  satellites  of  Jupiter  to  the  professors  in  Florence,  they 
would  neither  see  them  nor  the  telescope.  These  people  believe  there  is  no  truth 
to  seek  in  nature,  but  only  in  the  comparison  of  texts.' 


A  NEW  ASTRONOMY  223 

to  enlighten,  to  warm,  and  to  nourish  it.  What  are  these  parts  of  the 
microcosmos  ?  Two  nostrils,  two  eyes,  two  ears,  and  a  mouth.  So  in 
the  heavens,  as  in  a  macrocosmos,  there  are  two  favorable  stars,  two 
unpropitious,  two  luminaries,  and  Mercury  undecided  and  indifferent. 
From  this  and  many  other  similarities  in  nature,  such  as  the  seven 
metals,  etc.  which  it  were  tedious  to  enumerate,  we  gather  that  the 
number  of  planets  is  necessarily  seven.  Moreover,  these  satellites  of 
Jupiter  are  invisible  to  the  naked  eye,  and  therefore  can  exercise  no 
influence  on  the  earth,  and  therefore  would  be  useless,  and  therefore 
do  not  exist.  Besides,  the  Jews  and  other  ancient  nations,  as  well 
as  modern  Europeans,  have  adopted  the  division  of  the  week  into 
seven  days,  and  have  named  them  after  the  seven  planets.  Now, 
if  we  increase  the  number  of  the  planets,  this  whole  and  beautiful 
system  falls  to  the  ground/ — Fahie. 

It  was  inevitable  that  such  a  man  as  Galileo  should  accept  the 
Copernican  hypothesis.  He  writes  to  Kepler  in  1597 :  — 

'I  esteem  myself  fortunate  to  have  found  so  great  an  ally  in  the 
search  for  truth.  It  is  truly  lamentable,  that  there  are  so  few  who 
strive  for  the  true  and  are  ready  to  turn  away  from  wrong  ways  of 
philosophizing.  But  here  is  no  place  for  bewailing  the  pitifulness  of 
our  times,  instead  of  wishing  you  success  in  your  splendid  investiga- 
tions. I  do  this  the  more  gladly,  since  I  have  been  for  many  years 
an  adherent  of  the  Copernican  theory.  It  explains  to  me  the  cause 
of  many  phenomena  which  under  the  generally  accepted  theory  are 
quite  unintelligible.  I  have  collected  many  arguments  for  refuting  the 
latter,  but  I  do  not  venture  to  bring  them  to  publication. 

'  That  the  moon  is  a  body  like  the  earth  I  have  long  been  assured. 
I  have  also  discovered  a  multitude  of  previously  invisible  fixed  stars, 
outnumbering  more  than  ten  times  those  which  can  be  seen  by  the 
naked  eye,  —  forming  the  Milky  Way.  Further  I  have  discovered 
that  Saturn  consists  of  three  spheres  which  almost  touch  each 
other.' 

While  none  of  Galileo's  astronomical  discoveries  were  either 
necessary  or  sufficient  to  confirm  the  Copernican  theory,  their 
support  was  exceedingly  important.  Thus  the  slow  motion  of 
the  sun  spots  across  the  disc  and  their  subsequent  reappearance 


224  A  SHORT  HISTORY  OF  SCIENCE 

showed  rotation  of  that  body,  the  satellites  of  Jupiter  and  par- 
ticularly the  phases  of  Venus,  analogous  to  those  shown  by  the 
moon,  obviously  harmonized  with  the  Copernican  theory.  This 
implied  at  least  that  the  planets  shone  by  reflected  sunlight,  and 
it  had  indeed  been  insisted  against  that  theory  that  Venus  and 
Mercury  under  it  must  show  phases  till  then  undiscovered. 

In  1632  Galileo  published  his  celebrated  Dialogue  on  the  Two 
Chief  Systems  of  the  World,  the  Ptolemaic  and  the  Copernican, 
a  work  comparable  in  magnitude  and  importance  with  Copernicus' 
Revolutions.  In  the  curious  preface  he  says :  — 

'  Judicious  reader,  there  was  published  some  years  since  in  Rome  a 
salutiferous  Edict,  that,  for  the  obviating  of  the  dangerous  Scandals 
of  the  present  Age,  imposed  a  reasonable  Silence  upon  the  Pythag- 
orean Opinion  of  the  Mobility  of  the  Earth.  There  want  not  such  as 
unadvisedly  affirm,  that  the  Decree  was  not  the  production  of  a  sober 
Scrutiny,  but  of  an  illf ormed  passion ;  and  one  may  hear  some  mutter 
that  Consultors  altogether  ignorant  of  Astronomical  observations 
ought  not  to  clipp  the  wings  of  speculative  wits  with  rash  prohibitions. 
My  zeale  cannot  keep  silence  when  I  hear  these  inconsiderate  com- 
plaints. I  thought  fit,  as  being  thoroughly  acquainted  with  that 
prudent  Determination,  to  appear  openly  upon  the  Theatre  of  the 
World  as  a  Witness  of  the  naked  Truth.  ...  I  hope  that  by  these 
considerations  the  world  will  know  that  if  other  Nations  have  Navi- 
gated more  than  we,  we  have  not  studied  less  than  they;  and  that 
our  returning  to  assert  the  Earth's  stability,  and  to  take  the  contrary 
only  for  a  Mathematical  Capriccio,  proceeds  not  from  inadvertency 
of  what  others  have  thought  thereof,  but  (had  one  no  other  induce- 
ments), from  these  reasons  that  Piety,  Religion,  the  Knowledge  of  the 
Divine  Omnipotency,  and  a  consciousness  of  the  incapacity  of  man's 
understanding  dictate  unto  us/ 

In  the  first  of  the  four  conversations  into  which  the  work  is 
divided,  the  Aristotelian  theory  of  the  peculiar  character  of  the 
heavenly  bodies  is  subjected  to  destructive  criticism,  with  em- 
phasis on  such  phenomena  as  the  appearance  of  new  stars,  of 
comets  and  of  sun  spots,  the  irregularities  of  the  moon's  surface, 
the  phases  of  Venus,  the  satellites  of  Jupiter,  etc. 


Qrfl*  3 


GALILEO'S  DIALOGUE. 


A  NEW  ASTRONOMY  225 

'When  we  consider  merely  the  vast  dimensions  of  the  celestial 
sphere  in  comparison  with  the  littleness  of  our  earth  .  .  .  and  then 
think  of  the  speed  of  the  motion  by  which  a  whole  revolution  of  the 
heavens  must  be  accomplished  in  one  day,  I  cannot  persuade  myself 
that  the  heavens  turn  while  the  earth  stands  fast/ 

Adducing  not  merely  the  sun  spots  themselves,  but  their  rapid 
variation,  he  insists  that  the  universe  is  not  rigid  and  permanent, 
but  constantly  changing  or,  as  science  has  more  and  more  em- 
phasized since  his  day,  passing  through  consecutive,  related 
phases  or  evoking. 

'I  can  listen  only  with  the  greatest  repugnance  when  the  quality 
of  unchangeability  is  held  up  as  something  preeminent  and  complete 
in  contrast  to  variability.  I  hold  the  earth  for  most  distinguished 
exactly  on  account  of  the  transformations  which  take  place  upon  it.' 

He  begins  to  see  the  fallacy  of  the  objections  that  if  the  earth 
rotated,  a  body  dropped  from  a  masthead  would  be  left  behind 
by  the  ship  and  that  movable  objects  could  be  thrown  off  centrif- 
ugally  at  the  equator.  As  positive  arguments  in  support  of  the 
Copernican  system,  he  urges  particularly  the  retrogressions  and 
other  irregularities  of  the  planets,  and  also  the  tides. 

Of  the  famous  controversy  of  Galileo  with  the  Inquisition,  it 
may  here  suffice  to  quote  the  judgment  of  the  court  (see  Appen- 
dix) :  — 

'The  proposition  that  the  sun  is  in  the  centre  of  the  world  and 
immovable  from  its  place  is  absurd,  philosophically  false  and  formally 
heretical ;  because  it  is  expressly  contrary  to  the  Holy  Scriptures/  etc. 

and  a  passage  from  the  biographer  already  cited  at  so  much 
length :  — 

For  over  fifty  years  he  was  the  knight  militant  of  science,  and 
almost  alone  did  successful  battle  with  the  hosts  of  Churchmen  and 
Aristotelians  who  attacked  him  on  all  sides  —  one  man  against  a 
world  of  bigotry  and  ignorance.  If  then,  .  .  .  once,  and  only  once, 
when  face  to  face  with  the  terrors  of  the  Inquisition,  he,  like  Peter, 
denied  his  Master,  no  honest  man,  knowing  all  the  circumstances, 
will  be  in  a  hurry  to  blame  him. 
Q 


226  A  SHORT  HISTORY  OF  SCIENCE 

Of  Galileo's  still  more  remarkable  services  to  physics  and 
dynamics,  something  will  be  added  in  a  later  chapter. 

MEDICAL  AND  CHEMICAL  SCIENCES.  —  These  were  still  at  the 
low  medieval  level.  There  was  as  yet  no  scientific  medicine,  and 
no  chemistry  but  alchemy,  which  was  now  in  its  final  stage, 
iatro  (medical)  chemistry.  Here  one  great  name  is  that  of 
Paracelsus  (1493-1541),  erratic  and  radical  Swiss  physician  and 
alchemist,  whose  chief  merit  is  his  courage  in  opposing  mere 
authority  in  science,  and  whose  influence  long  after  caused 
"salt,  sulphur,  and  mercury"  to  be  highly  regarded  and  carefully 
studied.  He  also  introduced  and  insisted  upon  the  importance 
of  antimony  as  a  remedy,  and  is  said  to  have  been  the  first  to 
use  that  tincture  of  opium  which  is  still  known  by  his  name  for 
it;  viz.  laudanum.  Paracelsus,  on  the  other  hand,  in  spite  of 
the  fact  that  he  was  a  popular  surgeon,  rejected  the  study  of 
anatomy,  taught  medical  knowledge  through  scanning  of  the 
heavens,  and  considered  diseases  as  spiritual  in  origin.  "The 
true  use  of  chemistry,"  he  said,  "is  not  tolmake  gold  but  to 
prepare  medicines." 

Another  name  worthy  of  remembrance  in  the  chemistry  of  the 
sixteenth  century  is  that  of  Landmann  (Latin,  Agricola)  whose 
great  work  on  Metallurgy  (De  Re  Metallica,  1546)  is  the  most  im- 
portant of  this  period,  and  who  must  also  be  regarded  as  the 
first  mineralogist  of  modern  times/ 

ANATOMY.  VESALIUS. — Hardly  less  important,  meantime,  than 
the  studies  of  Copernicus,  Tycho  Brahe,  Galileo  and  Kepler  upon 
the  heavenly  bodies  were  those  of  the  Belgian  anatomist,  Andreas 
Vesalius,  upon  the  human  body.  For  more  than  1000  years  there 
had  been  almost  no  progress  in  anatomy  or  medicine,  Hippocrates 
and  Galen  being  still  regarded  as  the  final  authorities  in  these 
matters  up  to  the  middle  of  the  sixteenth  century.  Vesalius 
(1514-1564),  born  in  Brussels  and  educated  in  Paris,  was  the  first 
in  modern  times  to  dissect  the  human  body,  and  to  publish  excel- 
lent drawings  of  his  dissections.  It  was  said  that  he  opened  the 
body  of  a  nobleman  before  the  heart  had  entirely  ceased  beating, 
and  thereby  incurring  the  displeasure  of  the  Inquisition,  was  sen- 


BEGINNINGS  OF  MODERN  NATURAL  SCIENCE      227 

tenced  to  perform  a  penitential  journey  to  Jerusalem.  At  all 
events,  he  went  to  Jerusalem  and  was  shipwrecked  and  lost  while 
returning. 

After  Vesalius  the  study  of  human  anatomy  was  vigorously  and 
successfully  prosecuted  in  Italy  as  was  natural,  since  it  was  in  Italy 
that  Humanism  and  the  revival  of  learning  first  took  firm  hold 
of  Christian  Europe.  One  of  Vesalius'  Italian  contemporaries, 
Eustachius,  whose  name  is  still  familiarly  associated  with  the  pas- 
sage or  "tube"  connecting  the  throat  and  the  middle  ear,  is  hardly 
less  famous  in  the  history  of  anatomy  than  is  Vesalius  himself. 
The  name  of  Fallopius,  professor  at  Pisa  in  1548  and  at  Padua 
in  1551,  is  also  similarly  associated  with  the  human  oviducts, 
—  the  so-called  Fallopian  tubes.  His  disciple  Fabricius  of 
Acquapendente  discovered  the  valves  in  the  veins,  and  was  the 
teacher  of  William  Harvey.  A  Spanish  anatomist  of  note,  Michael 
Servetus, — born  1509, — perished  as  a  martyr  at  the  stake  in 
1553  because  of  heretical  writings  abhorrent  alike  to  the  In- 
quisition and  to  Calvin. 

Of  physiology  we  have  as  yet  little  or  no  account.  Doubtless 
all  the  anatomists  just  mentioned  and  many  other  "philosophers" 
had  pondered,  as  did  Aristotle  and  his  predecessors,  on  the  workings 
of  the  animal,  and  especially  the  human,  mechanism.  But  from 
Aristotle  (B.C.  322)  to  William  Harvey  (1578-1657)  no  real  progress 
was  made.  It  is  a  melancholy  commentary  on  superstition  and 
human  prejudice  that  long  after  the  brilliant  work  of  Vesalius  and 
the  Italian  anatomists,  no  proper  "anatomy  acts"  existed  to  make 
lawful  dissection  either  possible  or  easy,  so  that  for  several  cen- 
turies afterward  anatomists,  surgeons,  and  medical  students  felt 
themselves  at  times  obliged  to  resort  to  "body-snatching." 

NATUKAL  HISTORY  AND  NATURAL  PHILOSOPHY.  —  No  great 
progress  was  made  in  this  field  after  the  observations  of  Aristotle, 
Theophrastus,  Xenophanes,  and  Pythagoras  until  the  sixteenth 
century.  Fossils  mostly  remained  unexplained  or  were  regarded  as 
"  freaks  "  of  nature.  Animals  and  plants  were  comparatively  neg- 
lected and,  if  studied,  considered  either  as  the  raw  material  for  sup- 
posed remedies  or  medicines,  or  else  as  treated  by  Aristotle.  The 


228  A  SHORT  HISTORY  OF  SCIENCE 

twenty-six  books  De  Animalibus,  of  Albertus  Magnus  (d.  1282) 
were  not  printed  until  1478,  but  were  apparently  well  known  in 
manuscript  copies.  No  great  worker  appears  in  this  almost  neg- 
lected field  until  we  come  to  Conrad  Gesner  (or  Gessner)  (1516- 
1565),  the  first  famous  naturalist  of  modern  times,  on  account 
of  his  vast  erudition  surnamed  "the  German  Pliny."  Professor  of 
Greek  at  Lausanne  and  later  of  Natural  History  at  Basel,  he  was 
almost  as  prolific  an  author  as  was  della  Porta  fifty  years  later, 
for  he  wrote  extensively  upon  plants,  animals,  milk,  medicine, 
and  theology,  as  well  as  various  classical  subjects.  Yet  he  ranks 
high  in  the  history  of  biology,  both  for  the  extent  and  the  quality 
of  his  work  in  zoology  and  botany.  It  is  significant  that  Gesner 
was  a  Swiss,  and  as  such  probably  safe  from  persecution  at  a 
time  when  William  Turner,  an  English  ornithologist,  worked  and 
published  in  Cologne. 

At  the  end  of  the  fifteenth  and  beginning  of  the  sixteenth 
centuries  Leonardo  da  Vinci  (1452-1519)  turned  his  attention  in 
part  from  art  to  science,  engineering,  and  inventions,  making 
interesting  studies  in  architecture,  hydraulics,  geology,  etc.  He 
is  regarded  as  the  first  engineer  of  modern  times,  and  has 
been  called  "the  world's  most  universal  genius."  Palissy,  "the 
Potter,"  later  examined  minutely  various  fossils  and  took  the  then 
advanced  ground  (as  Xenophanes  and  Pythagoras  had  done, 
however,  some  two  thousand  years  earlier)  that  these  are  in 
reality  what  they  appear  to  be,  i.e.  petrified  remains  of  plant  and 
animal  life,  and  not  "freaks  of  nature."  Palissy's  bold  stand  on 
this  subject  marks  one  of  the  first  steps  in  modern  times  toward 
rational  geology. 

It  was  not  until  the  end  of  the  sixteenth  century,  when  Wil- 
liam Gilbert,  an  eminent  practising  physician  of  Colchester, 
England  (1540-1603),  published  his  now  famous  work  on  the 
magnet  (De  Magnete)  that  further  progress  was  made  through 
the  first  rational  treatment  of  electrical  and  magnetic  phenomena. 
To  him  is  due  the  name  electricity  (vis  electrica).  He  regarded 
the  earth  as  a  great  magnet  and,  accepting  the  Copernican 
theory,  attributed  the  earth's  rotation  to  its  magnetic  character. 


BEGINNINGS  OF  MODERN  NATURAL  SCIENCE      229 

He  even  extended  this  idea  to  the  heavenly  bodies,  with  an  ani- 
mistic tendency.  Gilbert  is  also  reputed  to  have  done  important 
work  in  chemistry,  but  none  of  this  has  survived. 

His  work  is  one  of  the  finest  examples  of  inductive  philosophy  that 
has  ever  been  presented  to  the  world.  It  is  the  more  remarkable 
because  it  preceded  the  Novum  Organum  of  Bacon,  in  which  the 
inductive  method  of  philosophizing  was  first  explained.  —  Thomas 
Thomson. 

The  most  prolific  writer  on  natural  philosophy  and  physical 
science  of  the  sixteenth  century  was  G.  della  Porta  (1543-1615), 
a  native  of  Naples  and  a  resident  of  Rome,  founder  of  an  early 
scientific  academy  there,  and  afterwards  of  the  famous  Accademia 
del  Lincei  of  Rome.  His  writings  are  voluminous  and  in  many 
books,  of  which  we  need  mention  here  only  his  Magia  Naturalis, 
(1569),  De  Refractione  (1593),  Pneumatica  (1691),  De  Distilla- 
tione  (1604),  De  Munitione  (1608)  and  De  Aeris  Transmutationi- 
bus  (1609). 

In  his  Natural  Magic,  della  Porta  is  the  first  to  describe  a 
camera  obscura,  besides  touching  on  many  interesting  properties 
of  lenses,  and  referring  to  spectacles,  some  forms  of  which  had 
long  been  known.  His  work  On  Refraction  deals  largely  with 
binocular  vision,  and  is  a  criticism  of  the  work  of  Euclid  and 
Galen  on  that  subject.  The  author  hints  also  at  a  crude  tele- 
scope, and  may  have  known  some  form  of  stereoscope.  Delia 
Porta 's  compositions  range  all  the  way  from  natural  magic  to 
Italian  comedies,  and  entitle  him  to  high  rank  as  a  tireless  and 
original,  if  not  especially  fruitful,  thinker  and  worker. 

REFERENCES  FOB  READING 

BERRY.     History  of  Astronomy.    Chapters  IV-VII. 

BREWSTER.     Martyrs  of  Science. 

DREYER.     Tycho  Brake ;  Planetary  Systems.     Chapters  XII-XVI. 

FAHIE.    Life  of  Galileo. 

GILBERT.     On  the  Magnet. 

LOCY.     Biology  and  its  Makers. 

LODGE.    Pioneers  of  Science. 


CHAPTER  XI 

PROGRESS   OF  MATHEMATICS  AND  MECHANICS  IN   THE 
SIXTEENTH   CENTURY 

IT  was  not  alone  the  striving  for  universal  culture  which  attracted 
the  great  masters  of  the  Renaissance,  such  as  Brunelleschi,  Leonardo 
da  Vinci,  Raphael,  Michael  Angelo  and  especially  Albrecht  Diirer,  with 
irresistible  power  to  the  mathematical  sciences.  They  were  conscious 
that,  with  all  the  freedom  of  the  individual  phantasy,  art  is  subject 
to  necessary  laws  and,  conversely,  with  all  its  rigor  of  logical  structure, 
mathematics  follows  esthetic  laws.  —  Rudio. 

The  miraculous  powers  of  modern  calculation  are  due  to  three 
inventions  :  the  Arabic  Notation,  Decimal  Fractions  and  Logarithms. 
—  Cajori. 

The  invention  of  logarithms  and  the  calculation  of  the  earlier  tables 
form  a  very  striking  episode  in  the  history  of  exact  science,  and,  with 
the  exception  of  the  Principia  of  Newton,  there  is  no  mathematical 
work  published  in  the  country  which  has  produced  such  important 
consequences,  or  to  which  so  much  interest  attaches  as  to  Napier's 
Descriptio.  —  Glaisher. 

It  is  Italy,  which  is  the  fatherland  of  Archimedes,  whose  creative 
power  embraces  all  domains  of  the  mechanical  science,  the  land  of 
the  Renaissance,  from  out  of  which  those  mighty  waves  of  new  ideas 
and  new  impulses  in  science  and  art  have  come  forth  into  the  world  — 
the  fatherland  of  Galileo  the  creator  of  experimental  physics,  of 
Leonardo  da  Vinci  the  engineer,  of  Lagrange  who  has  given  its  form 
to  modern  analytical  mechanics.  —  W.  v.  Dyck. 

Dynamics  is  really  a  product  of  modern  times,  and  affords  the 
rare  example  of  a  development  fulfilled  in  a  single  great  personage  — 
Galileo.  Nothing  is  finer  than  how  he,  beginning  in  the  'Aristotelian 
spirit,  gradually  frees  himself  from  its  bondage  and,  instead  of  empty 
metaphysics,  introduces  well-directed  methodical  investigations  of 
nature.  —  Timerding. 

The  period  from  the  invention  of  printing  about  1450  to  that  of 
analytic  geometry  in  1637  was  one  of  very  great  importance  for 
mathematics  and  mechanics  as  well  as  for  astronomy.  At  the 

230 


PROGRESS  OF  MATHEMATICS  AND   MECHANICS    231 

beginning,  Arabic  numerals  were  known,  but  the  mathematics 
even  of  the  universities  hardly  extended  beyond  the  early  books 
of  Euclid  and  the  solution  of  simple  cases  of  quadratic  equations 
in  rhetorical  form.  At  the  end  of  the  period  the  foundations 
of  modern  mathematics  and  mechanics  were  securely  laid. 

AIMS  AND  TENDENCIES  OF  MATHEMATICAL  PROGRESS.  —  In 
the  centuries  just  preceding,  the  chief  applications  of  mathematics 
had  connected  themselves  with  the  relatively  simple  needs  of  trade, 
accounts  and  the  calendar,  with  the  graphical  constructions  of  the 
architect  and  the  military  engineer,  and  with  the  sines  and  tangents 
of  the  astronomer  and  the  navigator.  During  the  period  in  ques- 
tion some  of  these  applications  became  increasingly  important, 
and  at  the  same  time  mathematics  was  more  and  more  cultivated 
for  its  own  sake.  Mathematicians  became  gradually  a  more  and 
more  distinctly  differentiated  class  of  scholars ;  mathematical  text- 
books took  shape.  The  beginnings  of  this  evolution  have  been 
dealt  with  already ;  its  further  progress  is  now  to  be  traced. 

The  larger  achievements  and  tendencies  of  the  period  in  mathe- 
matical science  were  the  following :  — 

In  Arithmetic,  decimal  fractions  and  logarithms  were  introduced, 
regulating  and  immensely  simplifying  computation;  a  general 
theory  of  numbers  was  developed ;  in  Algebra,  a  compact  and  ade- 
quate symbolism  was  worked  out,  including  the  use  of  the  signs 
-K  •*•>  X,  — ,  =,  (),  V  ,  and  of  exponents;  equations  of  the 
third  and  fourth  degree  were  solved,  negative  and  imaginary  roots 
accepted,  and  many  theorems  of  our  modern  theory  of  equations 
discovered. 

In  Geometry,  the  computation  of  TT  was  carried  to  many  deci- 
mals, the  beginnings  of  projective  geometry  were  made,  and  a 
so-called  method  of  indivisibles  developed,  foreshadowing  the 
integral  calculus;  in  plane  and  spherical  Trigonometry,  the 
theorems  and  processes  now  in  use  were  worked  out,  and  extensive 
tables  computed. 

In  Mechanics,  ideas  about  force  and  motion,  equilibrium  and 
centre  of  gravity,  were  gradually  clarified. 

Underlying  some  of  these  new  developments  are  the  dawning 


232  A  SHORT  HISTORY  OF  SCIENCE 

fundamental  concepts :  function,  continuity,  limit,  derivative,  in- 
finitesimal, on  which  our  modern  mathematics  has  been  built  up. 
Descartes,  Newton  and  Leibnitz  are  soon  to  make  their  revolu- 
tionary discoveries  in  analytic  geometry  and  the  calculus. 

We  have  seen  that  up  to  about  1500  the  chief  stages  in  the  de- 
velopment of  mathematics  have  been  the  introduction  and  im- 
provement of  Arabic  arithmetic  for  commercial  purposes  (though 
accounts  were  kept  in  Roman  numerals  until  1550  to  1650),  the 
rediscovery  of  Greek  geometry,  and  the  improvement  of  trigo- 
nometry in  connection  with  its  increasing  use  in  astronomy,  navi- 
gation and  military  engineering.  The  development  of  science  has 
been  powerfully  promoted  by  the  general  intellectual  emancipation 
of  the  Renaissance,  while  mathematical  progress,  beginning  earlier, 
has  been  both  a  cause  and  a  consequence  of  the  general  advance. 
The  diffusion  and  the  preservation  of  scientific  knowledge  have 
derived  immense  advantage  from  the  new  art  of  printing  and  from 
expanding  commercial  intercourse.  Algebra,  almost  helpless  in 
Greek  times  because,  for  lack  of  proper  symbolism,  expressed  only 
in  geometrical  or  rhetorical  form,  has  been  converted  by  a 
process  of  abbreviation,  at  first  into  a  syncopated  form,  inter- 
mediate between  the  rhetorical  and  our  modern  purely  symbolic 
notation. 

PACIOLI.  —  The  earliest  printed  book  on  arithmetic  and  algebra 
was  published  at  Venice  in  1494  by  Lucas  Pacioli,  a  Franciscan 
monk  born  in  Tuscany  about  1450.  Rules  are  here  given  for  the 
fundamental  operations  of  arithmetic,  and  for  extracting  square 
roots.  Commercial  arithmetic  is  treated  at  considerable  length 
by  the  newer  algoristic  or  Arabic  methods.  The  method  of  arbi- 
trary assumption  corrected  by  proportion  is  used  effectively,  for 
example :  — 

To  find  the  original  capital  of  a  merchant  who  spent  a  quarter 
of  it  in  Pisa  and  a  fifth  of  it  in  Venice,  who  received  on  these  transac- 
tions 180  ducats,  and  who  has  in  hand  224  ducats. 

Assume  that  his  original  capital  was  100  ducats ;  then  the  surplus 
would  be  100  —  25  —  20  =  55,  but  this  is  ^  of  his  actual  surplus 
224  —  180,  therefore  his  original  capital  was  f  of  100  =  80  ducats. 


PROGRESS  OF  MATHEMATICS  AND  MECHANICS    233 

Some  of  Pacioli's  commercial  problems  are  exceedingly  compli- 
cated. He  solves  numerical  equations  of  the  first  and  second 
degree,  but  admits  only  positive  roots  and  considers  the  solution 
of  cubic  equations,  as  well  as  the  squaring  of  the  circle,  impossible. 
Addition  is  denoted  by  p  or  p,  equality  sometimes  by  ae,  a  begin- 
ning of  syncopated  algebra.  The  introduction  of  the  radical  sign 
with  indices  V2>  V3  and  of  the  signs  +  and  —  date  from  about 
this  time. 

In  geometry  Pacioli,  like  Regiomontanus,  employs  algebraic 
methods.  Among  other  problems  he  determines  a  triangle  from 
the  radius  of  the  inscribed  circle  and  the  segments  into  which 
it  divides  one  of  the  sides.  His  solution,  though  highly  esteemed 
at  the  time,  is  much  less  simple  than  he  might  have  obtained  by 
the  formulas  at  his  command. 

In  the  spirit  of  the  Renaissance  he  brings  the  feeble  mathematics 
of  the  universities  into  fruitful  relations  with  the  practical  mathe- 
matics of  the  artist  and  the  architect.  The  inscribed  hexagon  and 
the  equilateral  triangle  play  their  part  as  gild  secrets  in  the  develop- 
ment of  Gothic  architecture.  The  question  is  not  "  How  to  prove," 
but  "How  to  do." 

On  the  other  hand,  the  current  tendency  to  drift  into  mysti- 
cal interpretation  is  exemplified  by  the  following  extract  from 
Pacioli :  — 

There  are  three  principal  sins,  avarice,  luxury,  and  pride;  three 
sorts  of  satisfaction  for  sin,  fasting,  almsgiving,  and  prayer;  three 
persons  offended  by  sin,  God,  the  sinner  himself,  and  his  neighbour; 
three  witnesses  in  heaven,  Pater,  verbum,  and  spiritus  sanctus;  three 
degrees  of  penitence,  contrition,  confession,  and  satisfaction,  which 
Dante  has  represented  as  the  three  steps  of  the  ladder  that  leads  to 
purgatory,  the  first  marble,  the  second  black  and  rugged  stone,  and  the 
third  red  porphyry.  There  are  three  sacred  orders  in  the  church 
militant,  subdiaconati,  diaconati,  and  presbyter ati  ;  there  are  three  parts 
not  without  mystery,  of  the  most  sacred  body  made  by  the  priest 
in  the  mass;  and  three  times  he  says  Agnus  Dei,  and  three  times, 
Sanctus;  and  if  we  well  consider  all  the  devout  acts  of  Christian  wor- 
ship, they  are  found  in  a  ternary  combination ;  if  we  wish  rightly  to 


234  A  SHORT  HISTORY  OF  SCIENCE 

partake  of  the  holy  communion,  we  must  three  times  express  our  con- 
trition, Domine  non  sum  dignus;  but  who  can  say  more  of  the  ternary 
number  in  a  shorter  compass,  than  what  the  prophet  says,  tu  signaculum 
sanctae  trinitatis.  There  are  three  Furies  in  the  infernal  regions; 
three  Fates,  Atropos,  Lachesis,  and  Clotho.  There  are  three  theo- 
logical virtues ;  Fides,  spes,  and  charitas.  Tria  sunt  pericula  mundi : 
Equum  currere;  navigare,  et  sub  tyranno  vivere.  There  are  three 
enemies  of  the  soul :  the  Devil,  the  world,  and  the  flesh.  There 
are  three  things  which  are  of  no  esteem :  the  strength  of  a  porter,  the 
advice  of  a  poor  man,  and  the  beauty  of  a  beautiful  woman.  There 
are  three  vows  of  the  Minorite  Friars;  poverty,  obedience,  and 
chastity.  There  are  three  terms  in  a  continued  proportion.  There 
are  three  ways  in  which  we  may  commit  sin :  corde,  ore,  ope.  Three 
principal  things  in  Paradise:  glory,  riches,  and  justice.  There  are 
three  things  which  are  especially  displeasing  to  God :  an  avaricious 
man,  a  proud  poor  man,  and  a  luxurious  old  man.  And  all  things 
in  short,  are  founded  in  three ;  that  is,  in  number,  in  weight,  and  in 
measure. 

GEOMETRY  IN  ART.  —  Brunelleschi  (1377-1446),  the  famous 
architect  of  the  early  Renaissance,  made  a  perspective  view  of  the 
Signoria  in  Florence  in  a  sort  of  box  with  clouds.  The  famous  doors 
of  the  Baptistery  by  his  contemporary  Ghiberti  show  the  develop- 
ment of  perspective  in  the  marked  contrast  between  the  earlier 
and  the  later  panels.  Raphael  in  his  School  of  Athens  includes 
himself  and  Bramante  in  a  group  of  mathematicians.  Painters 
were  even  called  for  a  time  perspectivists  —  prospettivi. 

Leonardo  da  Vinci  (1452-1519),  one  of  the  intellectual  giants 
of  the  Renaissance,  eminent  alike  in  art,  science  and  engineer- 
ing, gave  the  first  correct  explanation  of  the  partial  illumination 
of  the  darker  part  of  the  moon's  disc  by  reflection  from  the  earth. 
He  calls  mechanics  the  paradise  of  the  mathematical  sciences, 
because  through  it  one  first  gains  the  fruit  of  these  sciences.  He 
denies  the  possibility  of  perpetual  motion,  saying  "Force  is  the 
cause  of  motion  and  motion  the  cause  of  force."  He  discusses  the 
lever,  the  wheel  and  axle,  bodies  falling  freely  or  on  inclined  planes, 
foreshadowing  Galileo.  Contrary  to  the  Aristotelian  tradition  he 
asserts  that  everything  tends  to  continue  in  its  given  state,  and  he 


PROGRESS  OF  MATHEMATICS  AND  MECHANICS    235 

even  enunciates  the  fundamental  principle  that  for  simple  machines 
forces  in  equilibrium  are  inversely  as  the  virtual  velocities. 

'  Whoever/  he  says,  '  appeals  to  authority  applies  not  his  intellect 
but  his  memory/  '  While  Nature  begins  with  the  cause  and  ends  with 
the  experiment,  we  must  nevertheless  pursue  the  opposite  plan, 
beginning  with  the  experiment  and  by  means  of  it  investigating  the 
cause.'  'No  human  investigation  can  call  itself  true  science,  unless 
it  comes  through  mathematical  demonstration/  'He  who  scorns 
the  certainty  of  mathematics  will  not  be  able  to  silence  sophistical 
theories  which  end  only  in  a  war  of  words/ 

Unfortunately  his  work  in  this  field  remained  unpublished,  and 
therefore  relatively  unfruitful. 

Leonardo  and  other  great  artists  of  his  time  —  notably  Albrecht 
Durer  of  Nuremberg  (1471-1528)  —  developed  the  geometrical 
theory  of  perspective.  For  the  purpose  of  accurately  representing 
the  human  head  Diirer  made  both  plans  and  elevation.  "  Intelli- 
gent painters  and  accurate  artists,"  he  says,  "  at  the  sight  of  works 
painted  without  regard  to  true  perspective  must  laugh  at  the  blind- 
ness of  these  people,  because  to  a  right  understanding  nothing  im- 
presses more  disagreeably  than  falsehood  in  a  painting,  regardless 
of  the  diligence  with  which  it  has  been  made.  That  such  painters, 
however,  are  pleased  with  their  own  mistakes  is  due  to  the  fact 
that  they  have  not  learned  the  art  of  measurement,  without  which 
no  one  can  become  a  true  workman/'  All  this  had  importance 
both  for  modern  art  and  modern  geometry. 

Characteristic  of  this  period  is  the  so-called  Margarita  Philo- 
sophica  published  in  many  editions  from  1503  to  1600.  It  was  the 
first  modern  encyclopaedia  printed,  and  gives  in  its  twelve  books  "  a 
compendium  of  the  trivium,  the  quadrivium,  and  the  natural  and 
moral  sciences." 

A  younger  contemporary  of  Pacioli,  Michael  Stifel  (1487-1567), 
a  German  monk  converted  to  Lutheranism,  developed  a  fantastic 
arithmetical  interpretation  of  the  Bible,  identifying  Pope  Leo  X 
with  the  beast  in  Revelation  and  predicting  the  immediate  end 
of  the  world,  —  with  results  disastrous  to  his  person  as  well  as  his 
reputation. 


236  A  SHORT  HISTORY  OF  SCIENCE 

He  relates  .  .  .  that  whilst  a  monk  at  Esslingen  in  1520,  and  when 
infected  by  the  writings  of  Luther,  he  was  reading  in  the  library  of  his 
convent  the  13th  Chapter  of  Revelations,  it  struck  his  mind  that  the 
Beast  must  signify  the  Pope,  Leo  X ;  He  then  proceeded  in  pious  hope 
to  make  the  calculation  of  the  sum  of  the  numeral  letters  in  Leo 
decimus,  which  he  found  to  be  M,  D,  C,  L,  V,  I ;  the  sum  which  these 
formed  was  too  great  by  M,  and  too  little  by  X ;  but  he  bethought  him 
again,  that  he  has  seen  the  name  written  Leo  X ;  and  that  there  were 
ten  letters  in  Leo  decimus,  from  either  of  which  he  could  obtain  the 
deficient  number,  and  by  interpreting  the  M  to  mean  mysterium,  he 
found  the  number  required,  a  discovery  which  gave  him  such  un- 
speakable comfort,  that  he  believed  that  his  interpretation  must 
have  been  an  immediate  inspiration  of  God.  —  Peacock. 

Stif  el's  writings  on  arithmetic  and  algebra  embody  some  improve- 
ments of  current  notation.  He  introduced  for  example  the  symbols 
IA,  1AA,  IAAA  for  what  we  should  denote  by  x,  x2,  x*. 

The  low  state  of  computation  at  this  time  is  illustrated  with 
startling  clearness  by  a  bulletin  on  the  blackboard  at  Wittenberg, 
in  which  Melanchthon  urgently  invited  the  academic  youth  to 
attend  a  course  on  arithmetic,  adding  that  the  beginnings  of  the 
science  are  very  easy,  and  even  division  can  with  some  diligence  be 
comprehended. 

ROBERT  RECORDE  (1510-1558)  studied  at  Oxford  and  graduated 
in  medicine  at  Cambridge  in  1545,  later  becoming  "royal  physi- 
cian." His  "Grounde  of  Artes"  or  arithmetic,  one  of  the  earliest 
mathematical  books  printed  in  English  (1540),  ran  through  more 
than  27  editions  and  exerted  a  great  influence  on  English  education. 
In  the  "Preface  to  the  Loving  Reader"  he  says:  — 

Sore  ofttimes  have  I  lamented  with  myself  the  unfortunate  con- 
dition of  England,  seeing  so  many  great  Clerks  to  arise  in  sundry 
other  parts  of  the  World,  and  so  few  to  appear  in  this  our  Nation; 
whereas  for  pregnancy  of  natural  wit  (I  think)  few  Nations  do  excell 
English-men.  But  I  cannot  impute  the  cause  to  any  other  thing, 
then  to  the  contempt  or  misregard  of  Learning.  For  as  English-men 
are  inf eriour  to  no  men  in  mother  Wit,  so  they  pass  all  men  in  vain 
Pleasures,  to  which  they  may  attain  with  great  pain  and  labour ;  and 


PROGRESS  OF  MATHEMATICS  AND  MECHANICS    237 

are  slack  to  any  never  so  great  commodity,  if  there  hang  of  it  any  pain- 
full  study  or  travelsome  labour. 

The  book  itself  is  in  the  form  of  a  dialogue  or  catechism  be- 
ginning :  — 

The  Scholar  speaketh. 

'  Sir,  such  is  your  authority  in  mine  estimation,  that  I  am  content 
to  consent  to  your  saying,  and  to  receive  it  as  truth,  though  I  see 
none  other  reason  that  doth  lead  me  thereunto ;  whereas  else  in  mine 
own  conceit  it  appeareth  but  vain,  to  bestow  any  time  privately  in 
learning  of  that  thing  that  every  Child  may  and  doth  learn  at  all  times 
and  hours,  when  he  doth  any  thing  himself  alone,  and  much  more  when 
he  talketh  or  reasoneth  with  others/ 

He  employs  the  symbol  +  "whyche  betokeneth  too  muche,  as 
this  line  —  plaine  without  a  crosse  line  betokeneth  too  little." 

In  1557  he  published  an  algebra  under  the  alluring  title  "  Whet- 
stone of  Witte,"  using  the  sign  =  for  equality,  which  he  says  he 
selected  because  "noe  2  thynges  can  be  moare  equalle"  than 
two  parallel  straight  lines. 

ALGEBRAIC  EQUATIONS  OF  HIGHER  DEGREE. — Two  great  Ital- 
ian mathematicians  vied  with  each  other  in  giving  a  powerful  im- 
petus to  the  development  of  algebra  in  the  sixteenth  century. 

Niccolo  Fontana  or  TARTAGLIA  (1500-1557)  a  man  of  the  hum- 
blest origin,  lectured  at  Verona  and  Venice,  and  first  won  fame 
by  successfully  meeting  a  challenge  to  solve  mathematical  prob- 
lems, all  of  which  proved,  as  he  had  anticipated,  to  involve  cubic 
equations. 

His  Nova  Scienza  (1537)  discusses  falling  bodies,  and  many 
problems  of  military  engineering  and  fortification,  the  range 
of  projectiles,  the  raising  of  sunken  galleys,  etc. 

The  title-page  is  chiefly  occupied  by  a  large  plate,  which  represents 
the  courts  of  Philosophy,  to  which  Euclid  is  doorkeeper,  Aristotle  and 
Plato  being  masters  of  an  inmost  court,  in  which  Philosophy  sits 
throned,  Plato  declaring  by  a  label  that  he  will  let  nobody  in  who  does 
not  understand  Geometry.  In  the  great  court  there  is  a  cannon  being 
fired,  all  the  sciences  looking  on  in  a  crowd  —  such  as  Arithmetic, 


238  A  SHORT  HISTORY  OF  SCIENCE 

Geometry,  Music,  Astronomy,  Cheiromancy,  Cosmography,  Necro- 
mancy, Astrology,  Perspective,  and  Prestidigitation  !  A  wonderfully 
modest-looking  gentleman,  with  his  hand  upon  his  heart,  stands  among 
the  number,  with  a  you-do-me-too-much-honour  look  upon  his  coun- 
tenance; Arithmetic  and  Geometry  are  pointing  to  him,  and  under 
his  feet  his  name  is  written  —  Nicolo  Tartalea.  —  Morley,  Jerome 
Cardan. 

The  Inventioni  (1546)  gives  his  solution  of  the  cubic  equation. 
A  treatise  on  Numbers  and  Measures  (1556,  1560)  gives  a  method 
for  finding  the  coefficients  in  the  expansion  of  (1  +  x) n  for  n  =  2, 
...  6.  It  contains  also  a  wide  range  of  problems  from  commercial 
arithmetic  and  a  collection  of  mathematical  puzzles.  The  follow- 
ing examples  may  illustrate  these :  — 

'Three  beautiful  ladies  have  for  husbands  three  men,  who  are 
young,  handsome,  and  gallant,  but  also  jealous.  The  party  are 
travelling,  and  find  on  the  bank  of  a  river,  over  which  they  have  to 
pass,  a  small  boat  which  can  hold  no  more  than  two  persons.  How 
can  they  pass,  it  being  agreed  that,  in  order  to  avoid  scandal,  no 
woman  shall  be  left  in  the  society  of  a  man  unless  her  husband  is 
present  ? ' 

'A  ship  carrying  as  passengers  15  Turks  and  15  Christians  en- 
counters a  storm,  and  the  pilot  declares  that  in  order  to  save  the  ship 
and  crew  one  half  of  the  passengers  must  be  thrown  into  the  sea. 
To  choose  the  victims,  the  passengers  are  placed  in  a  circle,  and  it  is 
agreed  that  every  9th  man  shall  be  cast  overboard,  reckoning  from  a 
certain  point.  In  what  manner  must  they  be  arranged  so  that  the 
lot  may  fall  exclusively  upon  the  Turks?' 

'  Three  men  robbed  a  gentleman  of  a  vase  containing  24  ounces  of 
balsam.  Whilst  running  away  they  met  in  a  wood  with  a  glass-seller 
of  whom  in  a  great  hurry  they  purchased  three  vessels.  On  reaching  a 
place  of  safety  they  wish  to  divide  the  booty,  but  they  find  that  their 
vessels  contain  5,  11,  and  13  ounces  respectively.  How  can  they 
divide  the  balsam  into  equal  portions  ?  '  —  Ball. 

There  is  ho  other  treatise  that  gives  as  much  information  con- 
cerning the  arithmetic  of  the  sixteenth  century,  either  as  to 
theory  or  application.  The  life  of  the  people,  the  customs  of  the 


PROGRESS  OF  MATHEMATICS  AND  MECHANICS    239 

merchants,  the  struggles  to  improve  arithmetic,  are  all  set  forth 
here  by  Tartaglia  in  an  extended  but  interesting  fashion. 

Tartaglia,  anticipating  Galileo,  taught  that  falling  bodies  of 
different  weight  traverse  equal  distances  in  equal  times,  and  that 
a  body  swung  in  a  circle  if  released  flies  off  tangentially. 

GIROLAMO  CARDAN  (1501-1576)  led  a  life  of  wild  and  more  or 
less  disgraceful  adventure,  strangely  combined  with  various  forms 
of  scientific  or  semi-scientific  activity,  —  particularly  the  practice 
of  medicine.  He  studied  at  Pavia  and  Padua,  travelled  in  France 
and  England,  and  became  professor  at  Milan  and  Pavia. 

His  Ars  Magna  (1545)  contains  the  solution  of  the  cubic  equa- 
tion fraudulently  obtained  from  his  rival  Tartaglia.  After  its  publi- 
cation the  aggrieved  Tartaglia  challenged  Cardan  to  meet  him  in  a 
mathematical  duel.  This  took  place  in  Milan,  August  10,  1548, 
but  Cardan  sent  his  pupil  Ferrari  in  his  place.  Tartaglia  relates 
that  he  was  accompanied  only  by  his  brother,  Ferrari  by  many 
friends.  Cardan  had  left  for  parts  unknown.  As  Tartaglia  began 
to  explain  to  the  crowd  the  origin  of  the  strife  and  to  criticise 
Ferrari's  31  solutions,  he  was  interrupted  by  a  demand  that  judges 
be  chosen.  Knowing  no  one  present  he  declines  to  choose;  all 
shall  be  judges.  Being  finally  allowed  to  proceed  he  convicts  his 
opponent  of  an  erroneous  solution,  but  is  then  overwhelmed  by 
tumultuous  clamor  with  demands  that  Ferrari  must  have  the  floor 
to  criticise  his  solution.  In  vain  he  insists  that  he  be  allowed  to 
finish,  after  which  Ferrari  may  talk  to  his  heart's  content.  Fer- 
rari's friends  are  vehement ;  he  gains  the  floor  and  chatters  about  a 
problem  which  he  claims  Tartaglia  has  not  been  able  to  solve  till 
the  dinner  hour  arrives  and  Tartaglia,  apprehending  still  worse 
treatment,  withdraws  in  disgust. 

Ferrari  (1522-1565),  this  disciple  of  Cardan,  even  succeeded  in 
giving  a  general  solution  of  the  equation  of  the  fourth  degree, 
beyond  which,  as  has  been  shown  only  in  quite  recent  times,  the 
solution  can  in  general  no  longer  be  similarly  expressed. 

Some  idea  of  the  difficulty  of  these  sixteenth  century  achievements 
may  be  conveyed  by  the  corresponding  modernized  solutions.  If 
the  given  equation  is  ay?  +  by?  +  ex  +  d  =  0  the  coefficient  of  the 


240  A  SHORT  HISTORY  OF  SCIENCE 

first  term  is  made  1  by  division  and  that  of  the  second  is  made 

0  by  the  substitution  x  =  y  —  — .    The  new  equation  having  the  form 

6a 

e  $ 

f  +  ey  +/  =  0  we  now  put  y  =  z  -  — ,  whence  z3  -  — -  +/  =  0, 

O  Z  Zi  i  Z 

a  quadratic  equation  in  z3.  The  solution  of  the  original  equation  of 
degree  three  is  thus  made  to  depend  on  that  of  an  equation  of  degree 
one  less. 

Similarly  if  the  given  equation  of  the  fourth  degree  is  in  our 
notation  ax*  -f  6x3  +  ex2  +  dx  +  e  =  0  the  coefficient  of  the 
first  term  is  made  1  by  division  and  that  of  the  second  is  made  0  by 

the  substitution  x  =  y 

4a 

The  new  equation  having  the  form 
y*  +/2/2  +  gy  +  h  =0. 

We  put    y*  +fy*  +  gy  +  h  =  (y2  -  ay  +  0)  (y2  +  ay  +  y) 
whence          /  =  j8  -h  7  —  a2 

g  =  (0  -  T)  a 

h  =  07- 

We  obtain  a,  0,  7  from  these  three  equations  by  eliminating  two 
and  solving  the  cubic  equation  obtained  for  the  other ;  that  is,  the  solu- 
tion of  the  original  equation  of  degree  four  is  made  to  depend  on  that 
of  a  new  equation  of  degree  one  less. 

One  of  Cardan's  scientific  inventions  was  an  improved  suspen- 
sion of  the  compass  needle.  He  was  also  eminent  as  an  astrologer. 

SYMBOLIC  ALGEBRA  :  VIETA.  —  Of  still  greater  importance  in 
the  history  of  algebra  is  F.  Vieta  (1540-1603)  a  lawyer  of  the 
French  court.  He  won  the  interest  of  Henry  IV  by  solving  a  com- 
plicated problem  proposed  by  an  eminent  mathematician,  as  was 
the  custom  of  the  time,  as  a  challenge  to  the  learned  world.  This 
involved  an  equation  of  the  45th  degree  which  he  succeeded  in 
solving  by  a  trigonometric  device.  Later  he  was  employed  to  inter- 
pret the  cipher  despatches  of  the  hostile  Spaniards.  His  In  Artem 
Analyticam  Isagoge  is  the  earliest  work  on  symbolic  algebra. 
In  it  known  quantities  are  denoted  by  consonants,  unknown  by 
vowels,  the  use  of  homogeneous  equations  is  recommended,  the 


PROGRESS  OF  MATHEMATICS  AND   MECHANICS    241 

first  six  powers  of  a  binomial  given,  and  a  special  exponential 
notation  introduced.  He  shows  that  the  celebrated  classical 
problems  of  trisecting  a  given  angle  and  duplicating  a  cube  involve 
the  solution  of  the  cubic  equation,  and  makes  important  discoveries 
in  the  general  theory  of  equations  —  for  example  resolving  poly- 
nomials into  linear  factors  and  deriving  from  a  given  equation 
other  equations  having  roots  which  differ  from  those  of  the  first  by 
a  constant  or  by  a  given  factor.  He  solves  Apollonius'  famous 
problem  of  determining  the  circle  tangent  to  three  given  circles, 
and  expresses  TT  by  an  infinite  series.  He  devises  systematic 
methods  for  the  solution  of  spherical  triangles. 

DEVELOPMENT  OF  TRIGONOMETRY.  — Many  circumstances  com- 
bined to  promote  the  development  of  trigonometry  at  this  period. 
It  was  needed  by  the  military  engineer,  the  builder  of  roads,  the 
astronomer,  the  navigator,  and  the  mapmaker  whose  work  was 
tributary  to  all  of  these. 

Rheticus  (George  Joachim,  1514r-1576),  —  "the  great  computer 
whose  work  has  never  been  superseded,"  —  worked  out  a  table  of 
natural  sines  for  every  10  seconds  to  fifteen  places  of  decimals. 
We  owe  to  him  our  familiar  formulas  for  sin  1x  and  sin  3x.  The 
notation  sin,  tan,  etc.  and  the  determination  of  the  area  of  a 
spherical  triangle  date  from  about  this  time.  To  this  period  belong 
also  the  very  important  work  of  Mercator  on  map-making  and 
the  reform  of  the  calendar  by  Pope  Gregory  XIII. 

MAP-MAKING.  —  Mercator  (Gerhard  Kramer,  1512-1594)  de- 
voted himself  in  his  home  city,  Louvain,  to  mathematical  geogra- 
phy, and  gained  his  livelihood  by  making  maps,  globes  and 
astronomical  instruments,  combined  in  later  life  with  teaching. 
His  great  world  map,  completed  in  1569,  marks  an  epoch  in 
cartography.  The  first  "Atlas"  was  published  by  his  son  in  1595. 
He  gives  a  mathematical  analysis  of  the  principles  underlying  the 
projection  of  a  spherical  surface  on  a  plane. 

'If/  he  says,  'of  the  four  relations  subsisting  between  any  two 
places  in  respect  to  their  mutual  position,  namely  difference  of  latitude, 
difference  of  longitude,  direction  and  distance,  only  two  are  regarded, 
the  others  also  correspond  exactly,  and  no  error  can  be  committed  as 


242  A  SHORT  HISTORY  OF  SCIENCE 

must  so  often  be  the  case  with  the  ordinary  marine  charts  and  so  much 
the  more  the  higher  the  latitude/ 

Mercator's  geometrical  method  amounts  to  projecting  the 
spherical  surface  of  the  earth  on  a  cylinder  tangent  to  the  earth 
along  the  equator  and  having  the  same  axis  with  the  earth. 
Under  this  method  of  projection,  angles  are  preserved  in  magni- 
tude, but  areas  remote  from  the  equator  are  disproportionately 
expanded.  A  straight  line  on  the  chart  corresponds  with  the 
course  of  a  ship  steering  a  constant  course. 

THE  GREGORIAN  CALENDAR.  —  Until  1582  the  Julian  calendar 
(p.  143)  remained  in  force  with  365  J  days  each  year  and  a  gradually 
increasing  error  amounting  at  this  time  to  ten  days.  Under  the 
auspices  of  Pope  Gregory  the  days  from  October  5  to  15,  1572, 
were  dropped  and  the  number  of  leap-years  in  400  reduced  from 
100  to  97.  Religious  jealousies  prevented  the  adoption  of  this 
reform  in  Protestant  Germany  for  a  century,  while  England 
postponed  it  until  1752. 

A  NEW  INVENTION  FOR  COMPUTATION.  —  The  invention  of 
logarithms  would  appear  to  have  been  a  natural  sequel  of  any 
adequate  theory  and  notation  for  exponents.  Thus  Stifel  in  his 
arithmetic  (1544)  had  tabulated  small  integral  powers  of  2 — from 
J  to  64  —  and  shown  the  correspondence  between  multiplication 
of  these  powers  and  addition  of  the  indices  or  exponents,  but  his 
use  of  exponents  was  too  limited,  he  lacked  the  apparatus  of  deci- 
mal fractions  necessary  for  the  practical  application  of  the  method 
and  probably  had  no  conception  of  the  vast  labor-saving  possi- 
bilities so  near  at  hand. 

In  1614  John  Napier  published  at  Edinburgh  his  Mirifici  Logcb- 
rithmorum  Canonis  Descriptio,  for  which  the  time  was  so  fully  ripe 
that  an  enthusiastic  reception  was  at  once  assured.  Napier  as  a 
devout  Protestant,  stimulated  by  fear  of  an  impending  Spanish 
invasion,  busied  himself  with  inventions  "  proffitabill  &  necessary 
in  theis  dayes  for  the  defence  of  this  Hand  &  withstanding  of 
strangers  enemies  of  God's  truth  &  relegion."  Among  these  were 
a  mirror  for  burning  distant  ships,  and  a  sort  of  armored  chariot. 
Impressed  by  the  tremendous  calculations  then  in  progress  by 


PROGRESS  OF  MATHEMATICS  AND   MECHANICS    243 

Rheticus,  Kepler,  and  others  in  connection  with  the  development  of 
the  new  astronomy,  Napier  made  a  vastly  more  important  inven- 
tion. His  definition  of  a  logarithm  rests  on  the  following  kinetic 
basis  :  — 


T  S  is  a  straight  line  of  definite  length  ;  TI  Si  extends  to  the  right 
indefinitely.  Moving  points  P  and  PI  start  from  T  and  TI  with 
equal  initial  speeds;  the  latter  continues  at  the  same  rate,  the 
former  is  retarded  so  that  its  speed  is  always  proportional  to  its 
distance  from  S.  If  equal  intervals  are  taken  on  TI  Si  the  cor- 
responding intervals  in  TS  will  grow  smaller  to  the  right.  When  P 
is  at  any  position  Q  the  logarithm  of  QS  is  represented  by 
the  corresponding  length  TiQi  on  the  other  line.  It  may  be 
shown  in  fact  that  if  in  our  notation  PS  =  x,  TiPi  =  y,  TS  =  /, 

—  =  —  -.  This  conception  involving  a  functional  relation  be- 
dy  / 

tween  two  variables  went  much  deeper  than  the  comparison 
of  discrete  numbers  by  Stifel. 

Napier's  conception  of  a  logarithm  involved  a  perfectly  clear 
apprehension  of  the  nature  and  consequences  of  a  certain  functional 
relationship,  at  a  time  when  no  general  conception  of  such  a  relation- 
ship had  been  formulated,  or  existed  in  the  minds  of  mathematicians, 
and  before  the  intuitional  aspect  of  that  relationship  had  been  clarified 
by  means  of  the  great  invention  of  coordinate  geometry  made  later 
in  the  century  by  Rene  Descartes.  A  modern  mathematician  re- 
gards the  logarithmic  function  as  the  inverse  of  an  exponential  func- 
tion; and  it  may  seem  to  us,  familiar  as  we  all  are  with  the  use  of 
operations  involving  indices,  that  the  conception  of  a  logarithm 
would  present  itself  in  that  connection  as  a  fairly  obvious  one.  We 
must  however  remember  that,  at  the  time  of  Napier,  the  notion  of  an 
index,  in  its  generality,  was  no  part  of  the  stock  of  ideas  of  a  mathe- 
matician, and  that  the  exponential  notation  was  not  yet  in  use. 

—  Hobson. 


244 


A  SHORT  HISTORY  OF  SCIENCE 


Independent  tables  were  computed  by  the  astronomer  Biirgi 
and  published  at  Prague  in  1620.  Both  Napier  and  Biirgi,  basing 
their  work  on  the  relation  which  we  should  express  by  the  equiva- 
lent equations  x  =  ay  and  y  =  loga  x,  avoid  fractional  values  of  y  by 
taking  values  of  a  near  1,  their  actual  values  being  a  =  .9999999 
and  a  =  1 .0001  respectively.  In  choosing  a  base  less  than  1,  Napier 
is  also  influenced  by  his  desire  that  sines  and  cosines  as  proper 

fractions  shall  have  positive 
logarithms.  If  we  intro- 
duce our  modern  graphical 
interpretation  of  y  =  \ogax, 
Biirgi  is  concerned  with  the 
determination  of  abscissas 
of  points  where  the  exponen- 
tial curve  is  met  by  the 
horizontal  straight  lines  y 
=  c  where  c  takes  successive 
integral  values.  Choosing 
a  base  a  near  1  naturally  gives  values  of  x  near  each  other. 
Napier's  choice  of  a  base  less  than  1  would  correspond  with  the 
same  curve  inverted. 

In  1615  Henry  Briggs,  afterwards  Savilian  Professor  of  Geom- 
etry at  Oxford,  wrote  of  Napier  "  I  hope  to  see  him  this  summer, 
if  it  please  God,  for  I  never  saw  book  which  pleased  me  better,  or 
made  me  more  wonder."  In  connection  with  this  and  later  visits 
it  was  soon  discovered  that  great  simplification  in  the  practical 
use  of  logarithms  would  result  from  taking  log  1=0  and  log  10  =  1 
and  giving  up  the  restriction  of  logarithms  to  integral  values,  thus 
making  the  decimal  parts  of  all  logarithms  depend  wholly  on  the 
sequence  of  digits.  Napier  had  been  so  predominantly  interested  in 
trigonometric  applications  that  his  table  consisted  not  of  logarithms 
of  abstract  numbers,  but  of  7-place  logarithms  of  the  trigonometric 
functions  for  each  minute.  In  connection  with  his  change  of  the 
base,  Briggs  developed  interesting  methods  of  interpolating  and 
testing  the  accuracy  of  logarithms.  He  gives  the  logarithms  from 
1  to  20,000  and  from  90,000  to  100,000  to  14  places,  computing  also 
10-place  trigonometric  tables  with  an  angular  interval  of  10  seconds. 


PROGRESS  OF  MATHEMATICS  AND  MECHANICS    245 

Kepler  recognized  immediately  the  enormous  significance  of  the 
new  logarithmic  method  and  addressed  an  enthusiastic  panegyric 
to  Napier  in  1620,  not  knowing  that  he  had  died  in  1617.  What  if 
logarithms  had  been  invented  in  time  to  save  Kepler  his  vast  com- 
putations ? 

A  few  years  ago  we  have  been  shown  in  a  rectorial  address  what  the 
telescope  has  meant  for  observational  astronomy.  An  equally  great 
significance  attached  to  logarithms  for  the  computing  astronomer. 

—  Gutzmer. 

Vlacq  of  Leyden  soon  after  filled  the  gap  in  Briggs'  table,  and 
this  is  the  basis  for  the  tables  since  published.  The  first  tables  to 
base  e,  commonly  called  Napierian,  were  published  in  1619.  In 
more  recent  times  methods  of  interpolation  have  been  employed 
which  are  more  powerful  and  less  laborious,  while  ordinary  com- 
putation has  been  simplified  by  avoiding  the  use  of  too  many  deci- 
mal places,  and  by  the  mechanical  device  of  the  slide-rule.  The 
modern  computing  machine  naturally  tends  to  supersede  the 
logarithmic  method.  Among  the  remarkable  computations 
characteristic  of  the  sixteenth  century  may  be  mentioned  Ludolph 
von  Ceulen's  achievement  in  computing  TT  to  35  decimal  places, 
using  regular  polygons  of  96  and  192  sides.  German  writers  in 
consequence  have  sometimes  attached  his  name  to  this  important 
constant. 

In  England  Thomas  Harriott  (1560-1621)  and  William  Oughtred 
(1575-1660)  rendered  important  services  in  introducing  the  most 
recent  advances  in  arithmetic,  algebra  and  trigonometry.  The 
former  rejected  negative  and  imaginary  roots  indeed,  but  used 
the  signs  >  and  <,  denotes  a2  by  a  a,  etc.  Oughtred  uses  the 
symbols  X  and  : :,  also  the  contractions  for  sine,  cosine,  etc. 

"Two  NEW  BRANCHES  OF  SCIENCE."  —  Even  after  Galileo's 
condemnation  by  the  Inquisition,  though  old,  infirm,  and  nearly 
blind,  his  scientific  ardor  was  unquenched,  and  in  1638  he  pub- 
lished (at  Leyden)  a  work  on  mechanics  under  the  title,  Conver- 
sations and  Mathematical  Demonstrations  on  two  New  Branches 
of  Science,  which  constituted  the  most  notable  progress  in  mechan- 
ics since  Archimedes.  He  says : 


246  A  SHORT  HISTORY  OF  SCIENCE 

My  purpose  is  to  set  forth  a  very  new  science  dealing  with  a  very 
ancient  subject.  There  is,  in  nature,  perhaps  nothing  older  than 
motion,  concerning  which  the  books  written  by  philosophers  are  neither 
few  nor  small;  nevertheless  I  have  discovered  by  experiment  some 
properties  of  it  which  are  worth  knowing  and  which  have  not  hitherto 
been  either  observed  or  demonstrated.  Some  superficial  observations 
have  been  made,  as,  for  instance,  that  the  free  motion  (naturalem 
motum)  of  a  heavy  falling  body  is  continuously  accelerated ;  but  to 
just  what  extent  this  acceleration  occurs  has  not  yet  been  announced ; 
for  so  far  as  I  know,  no  one  has  yet  pointed  out  that  the  distances 
traversed,  during  equal  intervals  of  time,  by  a  body  falling  from  rest, 
stand  to  one  another  in  the  same  ratio  as  the  odd  numbers  beginning 
with  unity. 

It  has  been  observed  that  missiles  and  projectiles  describe  a 
curved  path  of  some  sort;  however  no  one  has  pointed  out  the  fact 
that  this  path  is  a  parabola.  But  this  and  other  facts,  not  few  in 
number  or  less  worth  knowing,  I  have  succeeded  in  proving ;  and  what 
I  consider  more  important,  there  have  been  opened  up  to  this  vast  and 
most  excellent  science,  of  which  my  work  is  merely  the  beginning,  ways 
and  means  by  which  other  minds  more  acute  than  mine  will  explore  its 
remote  corners. 

This  discussion  is  divided  into  three  parts;  the  first  part  deals 
with  motion  which  is  steady  or  uniform ;  the  second  treats  of  motion  as 
we  find  it  accelerated  in  nature;  the  third  deals  with  the  so-called 
violent  motions  and  with  projectiles.  .  .  . 

Throughout  this  work  Galileo  depends  on  results  of  experiment 
rather  than  on  mere  speculation.  He  recognizes  that  air  has 
weight  and  that  water  can  be  raised  but  a  certain  height  by 
the  ordinary  pump,1  but  he  still  accepts  the  ancient  notion  that 

1  '  This  pump  worked  perfectly  so  long  as  the  water  in  the  cistern  stood  above 
a  certain  level ;  but  below  this  level  the  pump  failed  to  work.  When  I  first  noticed 
this  phenomenon  I  thought  the  machine  was  out  of  order ;  but  the  workman  whom 
I  called  in  to  repair  it  told  me  the  defect  was  not  in  the  pump  but  in  the  water 
which  had  fallen  too  low  to  be  raised  through  such  a  height ;  and  he  added  that  it 
was  not  possible,  either  by  a  pump  or  by  any  other  machine  working  on  the  principle 
of  attraction,  to  lift  water  a  hair's  breadth  above  eighteen  cubits ;  whether  the 
pump  be  large  or  small  this  is  the  extreme  limit  of  the  lift.  Up  to  this  time  I  had  been 
so  thoughtless  that,  although  I  knew  a  rope,  or  rod  of  wood,  or  of  iron,  if  suffi- 
ciently long,  would  break  by  its  own  weight  when  held  by  the  upper  end,  it  never 
occurred  to  me  that  the  same  thing  would  happen,  only  much  more  easily,  to  a 


PROGRESS  OF  MATHEMATICS  AND  MECHANICS    247 

41  nature  abhors  a  vacuum"  as  an  explanation.  He  shows  experi- 
mentally that  a  body  descends  an  inclined  plane  with  uniformly 
accelerated  motion. 

In  a  board  12  ells  in  length  a  groove  half  an  inch  wide  was  made. 
It  was  drawn  straight  and  lined  with  very  smooth  parchment.  The 
board  was  then  raised  at  one  end,  first  one  ell,  then  two.  Then  Galileo 
let  a  polished  brass  ball  roll  through  the  groove  and  determined  the 
time  of  descent  for  the  whole  length  of  the  groove.  If  on  the  other  hand 
he  let  the  ball  roll  through  only  one  quarter  of  the  length,  this  required 
just  half  the  time.  .  .  .  The  distances  were  to  each  other  as  the 
squares  of  the  times, 

a  law  verified  by  hundredfold  repetitions  for  all  sorts  of  distances 
and  slopes.  The  time  was  still  determined  by  weighing  water 
escaping  through  a  small  orifice.  He  shows  by  ingenious  experi- 
ments the  dependence  of  velocity  on  height  alone,  and  that  a 
freely  falling  body  has  the  necessary  energy  to  reach  its  original 
level.  The  whole  theory  of  the  falling  body  is  now  easily  deduced. 

When,  therefore,  I  observe  a  stone  initially  at  rest  falling  from  an 
elevated  position  and  continually  acquiring  new  increments  of  speed, 
why  should  I  not  believe  that  such  increases  take  place  in  a  manner 
which  is  exceedingly  simple  and  rather  obvious  to  everybody?  If 
now  we  examine  the  matter  carefully  we  find  no  addition  or  increment 
more  simple  than  that  which  repeats  itself  always  in  the  same  manner. 
This  we  readily  understand  when  we  consider  the  intimate  relation- 
ship between  time  and  motion ;  for  just  as  uniformity  of  motion  is  de- 
fined by  and  conceived  through  equal  times  and  equal  spaces  (thus  we 
call  a  motion  uniform  when  equal  distances  are  traversed  during  equal 
time-intervals),  so  also  we  may,  in  a  similar  manner,  through  equal 
time-intervals,  conceive  additions  of  speed  as  taking  place  without 
complication ;  thus  we  may  picture  to  our  mind  a  motion  as  uniformly 
and  continuously  accelerated  when,  during  any  equal  intervals  of  time 
whatever,  equal  increments  of  speed  are  given  to  it.  ... 

Hence  the  definition  of  motion  which  we  are  about  to  discuss  may 

column  of  water.  And  really  is  not  that  thing  which  is  attracted  in  the  pump  a 
column  of  water  attached  at  the  upper  end  and  stretched  more  and  more  until 
finally  a  point  is  reached  where  it  breaks,  like  a  rope,  on  account  of  its  excessive 
weight?  .  .  .' 


248  A  SHORT  HISTORY  OF  SCIENCE 

be  stated  as  follows  :  A  motion  is  said  to  be  uniformly  accelerated,  when 
starting  from  rest,  it  acquires,  during  equal  time-intervals,  equal  in- 
crements of  speed.  .  .  . 

The  time  in  which  any  space  is  traversed  by  a  body  starting  from 
rest  and  uniformly  accelerated  is  equal  to  the  time  in  which  that  same 
space  would  be  traversed  by  the  same  body  moving  at  a  uniform  speed 
whose  value  is  the  mean  of  the  highest  speed  and  the  speed  just 
before  acceleration  began.  .  .  . 

The  spaces  described  by  a  body  falling  from  rest  with  a  uniformly 
accelerated  motion  are  to  each  other  as  the  squares  of  the  time- 
intervals  employed  in  traversing  these  distances.  .  .  . 

Galileo  passes  from  falling  bodies  to  pendulums,  in  which  the  fric- 
tion of  the  inclined  plane  is  absent  and  air  resistance  negligible. 
He  appreciates  the  possibility  of  utilizing  the  pendulum  for  time 
measurement,  and  devises  a  simple  apparatus  for  the  purpose, 
foreshadowing  the  invention  of  the  clock.  He  discovers  that  the 
time  of  vibration  of  the  pendulum  varies  as  the  square  root  of 
the  length. 

He  analyzes  correctly  the  component  motions  of  a  projectile, 
recognizing  the  law  of  the  parallelogram  of  motion,  as  distinguished 
from  the  parallelogram  of  forces  discovered  by  Newton.  He  shows 
that  whether  the  initial  direction  of  aim  is  horizontal  or  not,  the 
path  described  is  a  parabola  with  axis  vertical,  explicitly  neglecting 
air  resistance  and  change  of  direction  of  vertical  force. 

I  now  propose  to  set  forth  those  properties  which  belong  to  a  body 
whose  motion  is  compounded  of  two  other  motions,  namely,  one 
uniform  and  one  naturally  accelerated ;  these  properties,  well  worth 
knowing,  I  propose  to  demonstrate  in  a  rigid  manner.  This  is  the  kind 
of  motion  seen  in  a  moving  projectile ;  its  origin  I  conceive  to  be  as 
follows:  .  .  . 

A  projectile  which  is  carried  by  a  uniform  horizontal  motion  com- 
pounded with  a  naturally  accelerated  vertical  motion  describes  a 
path  which  is  a  semi-parabola.  —  Galileo,  Two  New  Sciences. 

All  this  Dynamics  was  practically  pioneer  work  of  enormous  im- 
portance for  the  future  of  mechanics. 


PROGRESS  OF  MATHEMATICS  AND  MECHANICS    249 

In  Statics  Galileo  had  somewhat  more  from  the  ancients  to 
build  upon.  To  him  we  owe  the  formulation  of  the  law  of  virtual 
velocities  —  applying  dynamical  ideas  to  problems  of  statics.  If 
two  forces  are  in  equilibrium  they  are  proportional  to  the  cor- 
responding paths,  or :  What  one  by  any  machine  gains  in  power 
is  lost  in  distance.  The  parallelogram  or  triangle  of  forces  in 
equilibrium  however  escapes  him,  and  his  ideas  about  impulse 
though  remarkably  in  advance  of  his  time  were  not  fully  worked 
out. 

He  investigates  strength  of  materials  under  tension  and  fracture, 
with  reference  to  practical  applications  in  construction.  He  draws 
just  inferences  in  regard  to  the  relation  between  strength  and 
size  of  plants  and  animals  as  well  as  machines,  comparing  for 
example  hollow  bones  and  straws  with  solid  bodies  of  similar  mass. 
He  derives  an  important  formula  for  the  stiffness  of  a  horizontal 
beam  supported  at  one  end  and  regarded  as  a  lever.  He  discusses 
the  curve  formed  by  a  cord  suspended  between  two  points,  recog- 
nizing that  it  is  not  a  parabola. 

In  Hydrostatics  he  reviews  the  known  work  of  Archimedes  and 
corrects  the  error  of  the  Aristotelians  in  regard  to  the  dependence 
of  floating  on  specific  gravity.  He  develops  the  modern  theory 
that  the  fundamental  factor  in  the  mechanics  of  fluids  is  that  they 
consist  of  freely  moving  particles  yielding  to  the  slightest  force. 
He  makes  effective  application  of  the  principle  of  virtual  velocities 
to  fluids.  At  the  close  of  his  third  conversation  he  expresses  his 
modest  confidence  in  the  great  future  of  his  new  ideas. 

The  theorems  set  forth  in  this  brief  discussion  will,  when  they 
come  into  the  hands  of  other  investigators,  continually  lead  to  wonder- 
ful new  knowledge.  It  is  conceivable  that  in  such  a  manner  a  worthy 
treatment  may  be  gradually  extended  to  all  the  realms  of  nature 

—  a    prediction   magnificently   fulfilled    in    succeeding    genera- 
tions. 

Among  other  branches  of  physics  in  which  Galileo  accomplished 
work  of  value  may  be  mentioned  the  expansion  by  heat  —  the 
beginnings  of  thermometry,  experiments  on  the  acoustics  of 


250  A  SHORT  HISTORY  OF  SCIENCE 

vibrating  cords  and  plates,  discovering  the  dependence  of  harmony 
on  the  ratio  of  the  rates  of  vibration,  and  the  relations  of  length, 
thickness,  and  tension  of  cords.  He  explains  resonance  and  dis- 
sonance. He  assumes  light  to  have  a  finite  velocity,  but  does 
not  succeed  in  measuring  it. 

Let  each  of  two  persons  take  a  light  contained  in  a  lantern,  or 
other  receptacle,  such  that  by  the  interposition  of  the  hand,  the  one 
can  shut  off  or  admit  the  light  to  the  vision  of  the  other.  Next  let 
them  stand  opposite  each  other  at  a  distance  of  a  few  cubits  and  prac- 
tice until  they  acquire  such  skill  in  uncovering  and  occulting  their 
lights  that  the  instant  one  sees  the  light  of  his  companion  he  will  un- 
cover his  own.  After  a  few  trials  the  response  will  be  so  prompt  that 
without  sensible  error  the  uncovering  of  one  light  is  immediately 
followed  by  the  uncovering  of  the  other,  so  that  as  soon  as  one  exposes 
his  light  he  will  instantly  see  that  of  the  other.  Having  acquired  skill, 
at  this  short  distance,  let  the  two  experimenters,  equipped  as  before, 
take  up  positions  separated  by  a  distance  of  two  or  three  miles  and 
let  them  perform  the  same  experiment  at  night,  noting  carefully 
whether  the  exposures  and  occultations  occur  in  the  same  manner  as 
at  short  distances ;  if  they  do,  we  may  safely  conclude  that  the  prop- 
agation of  light  is  instantaneous ;  but  if  time  is  required  at  a  distance 
of  three  miles  which,  considering  the  going  of  one  light  and  the  coming 
of  the  other,  really  amounts  to  six,  then  the  delay  ought  to  be  easily 
observable.  If  the  experiment  is  to  be  made  at  still  greater  distances, 
say  eight  or  ten  miles,  telescopes  may  be  employed,  each  observer 
adjusting  one  for  himself  at  the  place  where  he  is  to  make  the  experi- 
ment at  night ;  then  although  the  lights  are  not  large  and  are 
therefore  invisible  to  the  naked  eye  at  so  great  a  distance,  they  can 
readily  be  covered  and  uncovered  since  by  aid  of  the  telescopes,  once 
adjusted  and  fixed,  they  will  become  easily  visible.  .  .  . 

He  seeks  to  apply  to  astronomical  phenomena  the  new  discoveries 
in  magnetism. 

Everywhere  the  mathematical  and  inductive  method  became 
manifest  in  this  man.  Almost  all  domains  of  science  received  there- 
from the  most  powerful  impulse.  And  above  all  the  whole  field  of 
science  was  freed  from  the  outgrowths  of  metaphysical  modes  of 
thought  with  which  it  had  been  previously  so  overrun.  Galileo's 


PROGRESS  OF  MATHEMATICS  AND  MECHANICS    251 

individual  method  consisted  namely  in  always  conforming  to  the  limits 
of  scientific  investigation,  and  confining  his  attention  to  seizing  the 
phenomena  sharply  in  their  progress  and  in  their  relation  with  allied 
processes,  without  wandering  into  a  fruitless  search  after  the  ultimate 
bases  of  the  phenomena.  —  Dannemann. 

Such  a  limitation  has  been  of  the  highest  value  for  the  renewal  of 
natural  science  as  it  followed  at  the  beginning  of  the  seventeenth 
century. 

Galileo  was  not  chiefly  interested  in  mathematics,  but  he  em- 
phasizes the  dependence  of  other  sciences  upon  it. 

True  philosophy  expounds  nature  to  us;  but  she  can  be  under- 
stood only  by  him  who  has  learned  the  speech  and  symbols  in 
which  she  speaks  to  us.  This  speech  is  mathematics,  and  its  sym- 
bols are  mathematical  figures.  Philosophy  is  written  in  this  greatest 
book,  which  continually  stands  open  here  to  the  eyes  of  all,  but  can- 
not be  understood  unless  one  first  learns  the  language  and  characters 
in  which  it  is  written.  This  language  is  mathematics  and  the 
characters  are  triangles,  circles  and  other  mathematical  figures. 

He  gives  an  acute  discussion  of  infinite,  infinitesimal  and  con- 
tinuous quantities  leading  up  to  the  conclusion  "that  the  attri- 
butes '  larger/  '  smaller/  and  *  equal'  have  no  place  either  in 
comparing  infinite  quantities  with  each  other  or  in  comparing  in- 
finite with  finite  quantities."  Again  "the  finite  parts  of  a  con- 
tinuum are  neither  finite  nor  infinite  but  correspond  to  every  as- 
signed number." 

In  commenting  on  Galileo's  achievements,  Lagrange  the  great 
mathematician  of  the  eighteenth  century  says :  — 

These  discoveries  did  not  bring  to  him  while  living  as  much 
celebrity  as  those  which  he  had  made  in  the  heavens ;  but  to-day  his 
work  in  mechanics  forms  the  most  solid  and  the  most  real  part  of  the 
glory  of  this  great  man.  The  discovery  of  Jupiter's  satellites,  of  the 
phases  of  Venus,  and  the  Sun-spots,  etc.,  required  only  a  telescope  and 
assiduity ;  but  it  required  an  extraordinary  genius  to  unravel  the  laws 
of  nature  in  phenomena  which  one  has  always  under  the  eye,  but  the 
explanation  of  which,  nevertheless,  had  always  baffled  the  researches 
of  philosophers. 


252 


A  SHORT  HISTORY  OF  SCIENCE 


Leonardo  da  Vinci  likens  a  scientific  conquest  to  a  military  victory 
in  which  theory  is  the  field  marshal,  experimental  facts  the  soldiers. 
The  philosophers  who  preceded  Galileo  had,  in  the  main,  been  trying 
to  fight  battles  without  soldiers.  —  Crew. 

A  PIONEER  IN  MECHANICS.  STEVINUS. — Even  before  Galileo, 
Stevinus  of  Bruges  (1548-1620),  a  man  who  thought  independently 
on  mechanical  problems,  made  the  first  really  important  advances 
since  Archimedes,  eighteen  centuries  earlier.  Besides  engaging 
in  mercantile  pursuits  he  was  quartermaster-general  of  the 
Dutch  army,  and  an  authority  on  military  engineering.  He  was 
influential  in  improving  methods  of  public  statistics  and  account- 
ing, and  advocated  decimal  weights  and  measures.  Appreciating 
the  possibilities  of  the  decimal  fraction  he  asserted  (1585)  that 
fractions  are  quite  superfluous,  and  every  computation  can  be 
made  with  whole  numbers,  but  he  did  not  realize  the  simplest 
notation.  The  honor  of  this  great  invention  he  shares  with  Biirgi 
of  Cassel.  Another  of  his  inventions  was  a  sailing  carriage  carry- 
ing 28  people  and  outstripping  horses. 

In  a  treatise  on  Statics  and  Hydrostatics  (1586)  he  introduced 
comparatively  new  and  powerful  geometrical  methods  for  dealing 

with  mechanical  problems. 
Among  the  most  interesting  is. 
his  discussion  of  the  inclined 
plane  by  means  of  an  endless 
chain  hanging  freely  over  a  tri- 
angle with  unequal  sides.  Ex- 
cluding the  inadmissible  hy- 
pothesis of  perpetual  motion, 
the  uniform  chain  must  be  in 
equilibrium  in  any  position. 
The  hanging  portion  is  by  itself 
in  equilibrium,  therefore  the 
two  inclined  sections  must  bal- 
ance each  other,  and  either 
would  be  balanced  by  a  verti- 
Stevinus1  Triangle.  cal  force  corresponding  to  the 


PROGRESS  OF  MATHEMATICS  AND  MECHANICS    253 

altitude  of  the  triangle.  Arriving  thus  at  the  parallelogram  of 
forces  in  equilibrium,  he  expresses  his  astonishment  by  exclaim- 
ing "Here  is  a  wonder  and  yet  no  wonder." 

In  studying  pulleys  and  their  combinations  he  arrives  at  the 
far-reaching  result  that  in  a  system  of  pulleys  in  equilibrium  "the 
products  of  the  weights  into  the  displacements  they  sustain  are 
respectively  equal"  —  a  remark  containing  the  principle  of  virtual 
displacement.  He  reaches  correct  results  in  regard  to  basal  and 
lateral  pressure  by  reasoning  analogous  to  that  about  the  chain, 
and  by  assuming  on  occasion  that  a  definite  portion  of  the 
liquid  is  temporarily  solidified.  By  ingenious  experiments  he 
proves  the  dependence  of  fluid  pressure  on  area  and  depth, 
and  takes  proper  account  of  upward  and  lateral  pressure.  He 
studies  the  conditions  of  equilibrium  for  floating  bodies,  show- 
ing that  the  centre  of  gravity  of  the  body  in  question  must  lie 
in  a  perpendicular  with  that  of  the  water  displaced  by  it,  and 
that  the  deeper  the  centre  of  gravity  of  the  floating  body  the 
more  stable  is  the  equilibrium. 

In  analyzing  the  lateral  pressure  of  a  fluid  Stevinus  anticipates 
the  calculus  point  of  view  by  dividing  the  surface  into  elements  on 
each  of  which  the  pressure  lies  between  ascertainable  values.  In- 
creasing the  number  of  divisions,  he  says  it  is  manifest  that  one 
could  carry  this  process  so  far  that  the  difference  between  the  con- 
taining values  should  be  made  less  than  any  given  quantity  how- 
ever small  —  all  quite  in  harmony  with  our  present  definitions  of 
a  limit. 

Stevinus'  work  and  that  of  Galileo  seem  to  have  been  quite 
independent  of  each  other,  the  former  confining  his  theory  to 
statics,  the  latter  laying  a  solid  foundation  for  the  new  science 
of  dynamics.  Torricelli,  a  disciple  of  Galileo  best  known  for  his 
invention  of  the  mercurial  barometer,  extended  dynamics  to 
liquids,  studying  the  character  of  a  jet  issuing  from  the  side 
of  a  vessel. 

Throughout  this  period  the  universities  lagged.  In  Italy 
Galileo  lectured  to  medical  students  who  were  supposed  to  need 
astronomy  for  medical  purposes  —  i.e.  astrology.  At  Wittenberg 


254  A  SHORT  HISTORY  OF  SCIENCE 

there  was  a  professor  for  arithmetic  and  the  sphere,  and  one  for 
Euclid,  Peurbach's  planetary  theory  and  the  Almagest,  but  their 
students  were  few.  .  .  .  So,  says  a  German  writer,  we  face  the 
extraordinary  fact  that  the  most  educated  of  the  nation  were  as 
helpless  in  the  problems  of  daily  life  as  a  marketwoman  of  to-day. 
The  university  lectures  in  mathematics  were  mainly  confined 
to  the  most  elementary  computation,  —  matters  taught  more 
thoroughly  in  the  commercial  schools,  particularly  after  the 
invention  of  printing. 

GIORDANO  BRUNO  (1548-1600). — In  the  Appendix  will  be 
found  the  judgment  and  sentence  of  the  Inquisition  upon 
Galileo,  together  with  his  recantation,  —  one  of  the  darkest  pages 
in  the  history  of  Science.  Another  victim  of  the  Inquisition  was 
Bruno,  an  Italian  philosopher,  who,  having  joined  the  Dominican 
order  at  the  age  of  fifteen,  was  later  accused  of  impiety  and  sub- 
jected to  persecution.  Bruno  fled  from  Rome  to  France,  and 
later  to  England,  where  at  Oxford  he  disputed  on  the  rival  merits 
of  the  Copernican  and  the  so-called  Aristotelian  systems  of  the 
universe.  In  1584  he  published  an  exposition  of  the  Copernican 
theory.  Bruno,  moreover,  attacked  the  established  religion,  jeered 
at  the  monks,  scoffed  at  the  Jewish  records,  miracles,  etc.,  and 
after  revisiting  Paris,  and  residing  for  a  time  in  Wittenberg,  rashly 
returned  to  Italy,  where  he  was  apprehended  by  the  Inquisition 
and  thrown  into  prison.  After  seven  years  of  confinement  he 
was  excommunicated  and,  on  Feb.  17,  1600,  burnt  at  the  stake. 
In  1889  a  statue  in  his  honor  was  unveiled  in  Rome  at  the  place 
of  his  execution,  the  Square  of  the  Flower  Market.  Thus  was 
the  end  of  the  sixteenth  century  illuminated  by  the  flames  of 
martyrdom. 

REFERENCES  FOR  READING 

BALL.     Short  History  of  Mathematics,  Chapters  XII,  XIII. 

FAHIE.    Life  of  Galileo. 

GALILEO  GALILEI.     Two  New  Sciences.    (Translated  by  Crew  and  De  Salvio.) 

HOBSON.     John  Napier  and  the  Invention  of  Logarithms. 

LODGE.     Pioneers  of  Science  (Galileo) . 

MACH.     Science  of  Mechanics  (for  Galileo  and  Stevinus). 

MORLEY.     Life  of  Cardan. 


CHAPTER  XII 

NATURAL  AND   PHYSICAL   SCIENCE   IN   THE   SEVEN- 
TEENTH  CENTURY 

THE  CIRCULATION  OF  THE  BLOOD  :  HARVEY  (1578-1657). — The 
blood  has  always  been  regarded  as  one  of  the  principal  parts  of 
the  body.  Hippocrates  considered  it  one  of  his  four  great 
"humors,"  and  in  the  Hebrew  Scriptures  it  is  stated  that  "the 
blood  ...  is  the  life."  Yet  up  to  the  seventeenth  century  nothing 
definite  was  known  of  its  movements  throughout  the  body.  That 
it  was  under  pressure  must  have  been  known,  for  it  flowed  or 
"escaped "  freely  from  wounds,  and  flow  results  only  from  pressure 
of  some  sort,  while  escape  is  relief  from  detention.  The  arteries 
had  been  misinterpreted  for  centuries  and  were  early  considered  to 
be  air  tubes,  because  they  were  studied  only  after  death  when  as 
we  now  know  they  are  empty.  Even  the  dissections  of  the  anato- 
mists of  the  sixteenth  century  had  failed  to  reveal  the  complete  and 
true  office  of  the  arteries,  and  it  remained  for  Harvey,  an  English 
pupil  of  the  Italian  anatomist  Fabricius,  to  make  —  largely 
through  the  vivisection  of  animals  and  observation  of  the  heart 
and  arteries  in  actual  operation  —  discoveries  of  basic  importance 
in  anatomy,  physiology,  embryology,  and  medicine  (see  Appendix). 

While  working  in  Italy,  Harvey  learned  of  and  doubtless  saw 
the  valves  in  the  veins  which  were  discovered  by  Fabricius.  These 
valves  are  thin  flaps  of  tissue  so  placed  as  to  check  the  flow  of  blood 
in  one  direction  while  offering  no  resistance  to  that  flowing  the  other 
way.  On  his  return  to  England,  Harvey  apparently  pondered  on 
the  function  of  these  valves  and  saw  that  they  could  be  of  use  only 
by  permitting  the  flow  of  the  blood  in  one  direction  while  prevent- 
ing its  movement  in  the  opposite  direction.  At  this  time  it  was 
supposed  that  the  blood  simply  oscillated,  or  moved  back  and  forth 

255 


256  A  SHORT  HISTORY  OF  SCIENCE 

like  a  pendulum,  a  view  which,  if  the  valves  had  any  meaning, 
was  now  plainly  untenable.  Harvey  therefore  set  to  work  to 
study  the  beating  of  the  heart  and  the  flowing  of  the  blood,  and 
soon  came  to  the  conclusion  that  there  must  be  a  steady  flow  or 
streaming  in  one  direction,  and  not  an  oscillation  back  and  forth 
as  was  generally  supposed.  But  to  prove  was  here,  as  always, 
harder  than  to  believe,  and  much  time  and  labor  were  required  to 
settle  the  question.  At  length,  however,  by  dissections  and  vivi- 
sections of  the  lower  animals,  and  after  publishing  (in  1628)  a  bro- 
chure presenting  his  facts  and  meeting  objections,  Harvey  suc- 
ceeded, with  the  result  that  his  name  justly  stands  to-day  beside 
those  of  the  Greek  and  Alexandrian  Fathers  of  Medicine,  Hippoc- 
rates and  Galen.  It  is  one  of  the  ironies  of  fate  that  while  Harvey 
rightly  reasoned  from  circumstantial  evidence  that  the  blood  must 
steadily  flow  from  the  arteries  to  the  veins,  he  himself  never  actually 
saw  that  flowing,  —  a  sight  which  any  schoolboy  may  now  see, 
but  impossible  before  the  introduction  of  the  microscope,  and  first 
enjoyed  by  Malpighi  in  1661,  only  four  years  after  Harvey's  death. 

In  embryology,  also,  Harvey  proved  himself  an  original  and 
penetrating  observer.  In  his  day  and  earlier  it  was  supposed  that 
the  embryo,  in  the  hen's  egg,  for  example,  exists  even  at  the  very 
outset  as  a  perfect  though  extremely  minute  chick,  with  all  its  parts 
complete.  This  " preformation"  theory  was  opposed  by  Harvey, 
whose  doctrine  of  "epigenesis"  was  substantially  that  of  modern 
embryology :  viz.  that  the  embryo  chick  is  gradually  formed  by 
processes  of  growth  and  differentiation  from  comparatively  simple 
and  undifferentiated  matter,  somehow  set  apart  and  prepared  in 
the  body  of  the  parents. 

ATMOSPHERIC  PRESSURE  :  TORRICELLI'S  BAROMETER.  —  The 
problem  of  the  existence  and  nature  of  voids  and  vacua  had  always 
been  an  interesting  puzzle  for  philosophers.  The  Greeks  assumed 
the  existence  of  empty  spaces  or  "voids,"  and  as  late  as  the  age  of 
Elizabeth  it  was  the  orthodox  belief  that  "nature  abhors  a 
vacuum."  Galileo,  even,  held  to  it  in  1638.  (Cf.  p.  246.) 

Evangelista  Torricelli  (1608-1647),  inspired  by  the  Dialogues  of 
Galileo  (1638),  published  on  Motion  and  other  subjects  in  1644. 


NATURAL  SCIENCE  IN  SEVENTEENTH  CENTURY    257 

He  resided  with  Galileo  and  acted  as  his  amanuensis  from  1641 
until  Galileo's  death.  In  experimenting  with  mercury  he  found 
that  this  did  not  rise  to  33  feet,  but  instead  to  hardly  as  many 
inches.  He  next  proved,  by  comparing  the  specific  gravity  of 
water  and  mercury,  that  the  same  "pressure"  was  at  work  in 
both  cases,  and  boldly  affirmed  that  this  pressure  was  that  of  the 
atmosphere.  The  tube  of  mercury  used  in  his  experiments  was 
what  we  now  call  a  barometer  (baros,  weight),  but  it  was  for  a 
long  time  called  "the  Torricellian  Tube,"  as  the  empty  space 
above  the  mercury  is  still  called  the  "Torricellian  vacuum." 
This  invention  or  discovery  of  Torricelli's  was  one  of  the  most 
fertile  ever  made,  for  at  one  blow  it  demolished  the  ancient  super- 
stition that  "nature  abhors  a  vacuum,"  explained  very  simply 
two  ancient  puzzles  (why  water  rises  in  a  pump,  and  why  it  rises 
only  33  feet),  determined  accurately  the  weight  of  the  atmosphere, 
proved  it  possible  to  make  a  vacuum,  and  gave  to  mankind  an 
entirely  new  and  invaluable  instrument,  the  barometer.  Torri- 
celli's results  and  explanations  were  received  at  first  with  incredu- 
lity, but  were  soon  confirmed,  notably  by  Pascal  (1623-1662) 
in  a  treatise,  New  Experiments  on  the  Vacuum.  In  one  of  these 
Pascal  used  wine  instead  of  water  or  mercury  in  the  Torricellian 
tube,  with  satisfactory  results,  and  in  another,  reasoning  that  if 
Torricelli  were  right,  liquids  in  the  tube  should  stand  lower  on  a 
mountain  than  in  a  valley,  persuaded  his  brother-in-law,  Perier, 
to  ascend  the  Puy  de  Dome  (near  Clermont,  France)  in  September, 
1648,  on  which  mountain  the  column  was  found  to  be  much 
shorter.  This  and  other  brilliant  work  by  Pascal  have  given  him 
a  high  rank  among  natural  philosophers. 

Since  it  was  now  easy  to  obtain  a  vacuum  by  the  Torricellian 
experiment,  fresh  attempts  were  made  to  produce  vacua  otherwise. 
Von  Guericke,  burgomaster  of  Magdeburg  in  Hannover,  after 
many  failures,  finally  succeeded  in  pumping  the  air  out  of  a  hollow 
metallic  globe.  It  was  in  this  experiment  that  the  air-pump  was 
introduced.  Guericke  found  that  his  globe  had  to  be  very  strong 
to  resist  crushing  by  the  atmospheric  pressure,  and  in  the  popular 
demonstration  now  known  as  that  of  the  Magdeburg  hemi- 


258  A  SHORT  HISTORY  OF  SCIENCE 

spheres  he  showed  that  eight  horses  on  either  side  were  unable  to 
overcome  this  pressure  on  a  particular  globe  which  he  had  con- 
structed and  exhausted  of  air.  These  various  experiments  and  dis- 
coveries relating  to  atmospheric  pressure  led  to  the  investigations 
and  laws  of  Boyle,  Mariotte,  and  others  and,  less  than  a  century 
later,  to  the  steam-engine  of  Watt,  in  which  steam  was  at  first 
used  only  to  produce  a  vacuum,  —  atmospheric  pressure  being 
employed  as  the  moving  force. 

FURTHER  STUDIES  OF  THE  ATMOSPHERE  :  GASES.  —  Meantime 
the  chemical  composition  of  the  atmosphere  was  being  no  less 
eagerly  studied.  Robert  Boyle  (1627-1691)  published  at  Oxford 
in  1660,  New  Experiments  Physico-Mechanical  touching  the 
Spring  of  the  Air  and  its  Effects,  and  in  his  Sceptical  Chymist 
gives  an  interesting  and  instructive  picture  of  the  chemical  ideas 
of  his  time.  He  was  the  first  to  insist  on  the  difference  between 
compounds  and  mixtures,  and  probably  the  first  to  use  the  pneu- 
matic trough  for  the  collection  and  study  of  gases. 

The  word  "gas"  was  introduced  by  Van  Helmont  (1577-1644), 
who  by  virtue  of  the  following  remarkable  statement  deserves  to- 
be  remembered  as  the  principal  chemist  of  the  earlier  half  of  the 
seventeenth  century :  — 

Charcoal  and  in  general  those  bodies  which  are  not  immediately  re- 
solved into  water,  disengage  by  combustion  spiritum  syhestrum.  From 
62  Ibs.  of  oak  charcoal  1  Ib.  of  ash  is  obtained,  therefore  the  remaining 
61  Ibs.  are  this  spiritum  syhestre.  This  spirit,  hitherto  unknown,  I 
call  by  the  new  name  of  gas.  It  cannot  be  enclosed  in  vessels  or  re- 
duced to  a  visible  condition.  There  are  bodies  which  contain  this 
spirit  and  resolve  themselves  entirely  into  it :  in  these  it  exists  in  a 
fixed  or  solidified  form,  from  which  it  is  expelled  by  fermentation,  as  we 
observe  in  wine,  bread,  etc. 

It  has  been  well  said  that 

this  passage  is  remarkable  not  only  for  the  explicit  mention  of  car- 
bonic acid  gas  (as  we  now  call  it)  as  a  product  of  fermentation,  and  for 
the  introduction  of  the  word  gas  for  the  first  time,  but  also  for  its  ap- 
peal to  the  balance, 


NATURAL  SCIENCE  IN  SEVENTEENTH  CENTURY    259 

the  formal  introduction  of  which  into  chemistry  was  only  made  a 
century  later  by  Lavoisier.  Van  Helmont  also  points  out  that  his 
gas  syhestre  is  produced  by  the  action  of  acids  on  shells,  is  en- 
gendered in  putrefaction  and  combustion,  and  is  present  in  caves, 
mines,  and  mineral  waters.  In  these  ideas  and  passages  we  find  an 
agreeable  departure  from  the  mysticism  of  the  alchemists  and  the 
wild  surmises  of  Paracelsus.  At  the  same  time  Van  Helmont's 
ideas  in  other  directions  were  crude  enough,  since  he  is  credited  with 
a  recipe  for  the  artificial  production  of  mice  from  "corn  and  sweet 
basil." 

FROM  PHILOSOPHY  TO  EXPERIMENTATION.  —  The  seventeenth 
century  differs  from  all  before  it  in  the  increasing  attention  paid 
to  experimental  science.  From  the  philosophizing  of  Paracelsus 
and  Gilbert  it  is  agreeable  to  pass  to  the  experimental  work  of 
Harvey,  Torricelli  and  in  chemical  inquiries  to  Van  Helmont,  whose 
logical  successor  is  Robert  Boyle  (1627-1691),  already  mentioned 
for  his  work  on  the  resistance,  or  "spring,"  of  the  atmosphere,  etc. 
Among  many  other  ingenious  experiments  Boyle  worked  on  evapo- 
ration, in  air  and  in  vacua;  on  boiling  and  on  freezing;  and  on 
the  effects  of  exposing  animals  to  the  diminished  atmospheric  pres- 
sure produced  by  the  air-pump.  In  this  direction  he  was  the 
first  to  prove  that  fishes  require  air  dissolved  in  the  water  in 
which  they  live.  He  also  studied  the  rusting  of  metals  —  a 
problem  then  widely  discussed  —  and  from  all  his  studies  con- 
cludes that  there  is  in  the  atmosphere  some  vital  substance  which 
plays  a  principal  part  in  such  phenomena  as  combustion,  respira- 
tion, and  fermentation.  When  this  substance  has  once  been  con- 
sumed, flame  is  instantly  extinguished,  and  yet  the  air  from  which 
it  has  gone  seems  nearly  intact.  He  wrote  a  treatise  entitled,  Fire 
and  Flame  weighed  in  a  Balance,  in  which  he  described  the  increase 
of  weight  of  metals  on  calcination.  But  as  he  got  about  the  same 
results  whether  the  crucible  was  open  or  shut,  he  was  misled  into 
the  belief  that  the  air  had  little  to  do  with  his  results,  which  he 
attributed  rather  to  the  fixation  of  the  "fire"  by  the  porous 
crucibles.  In  these  and  Boyle's  other  experiments  it  is  plain  that 
we  are  rapidly  moving  from  alchemical  and  iatro-chemical  stages 


260  A  SHORT  HISTORY  OF  SCIENCE 

toward  the  modern  experimental  period  of  chemistry,  of  which  he 
and  Van  Helmont  are  the  pioneers.  Neither,  however,  while  work- 
ing on  air  greatly  advanced  our  ideas  of  atmospheric  chemistry. 

The  atmosphere  in  its  relation  to  combustion  and  respiration  was 
further  studied  by  an  English  physician,  Dr.  John  Mayow  (1645- 
1679),  who  made  many  experiments  upon  the  shrinkage  of  air- 
volume  during  the  burning  of  camphor  and  other  substances  and 
during  the  confinement  of  mice  under  a  bell-glass.  The  dying  of 
the  mice  and  the  cessation  of  the  combustion,  which  after  a  time 
ensued,  he  attributed  to  the  exhaustion  of  some  ingredient  in  the 
air  indispensable  to  life  and  combustion.  This  ingredient,  which 
we  now  call  oxygen,  Mayow  named  "fire-air." 

Very  soon,  however,  a  new  theory  of  combustion  (and  as  it 
turned  out  a  false  theory)  began  to  absorb  the  attention  of 
natural  philosophers. 

FROM  ALCHEMY  TO  CHEMISTRY.  —  The  saying  is  attributed  to 
Liebig  that  "Alchemy  was  never  at  any  time  different  from 
chemistry."  In  one  sense  this  is  undoubtedly  true.  The  search 
for  "the  philosopher's  stone,"  "the  elixir  of  life,"  "potable  gold," 
and  the  "transmutation  of  metals,"  consisted  of  necessity  in  the 
use  of  processes  such  as  boiling,  baking,  wetting,  drying,  evaporat- 
ing, condensing,  burning,  calcifying,  decalcifying,  acidifying, 
freezing,  melting,  and  the  like,  mostly  tending  towards  chemical 
changes  and  the  formation  of  new  mixtures  and  compounds.  But 
even  if  Liebig's  saying  were  true,  chemistry  has  passed  through 
three  principal  stages ;  viz.  first,  purely  empirical  experimenting, 
mostly  for  practical  purposes,  whether  metallurgical  or  other; 
second,  an  iatro-chemical  or  medico-chemical  phase ;  and  finally 
the  really  scientific  period  of  to-day,  the  way  for  which  may  be 
said  to  have  been  cleared  by  the  Sceptical  Chymist  of  Robert 
Boyle,1  first  published  in  English  in  Oxford  in  1661.  In  this  re- 

1  The  Hon.  Robert  Boyle  was  one  of  the  most  active,  perhaps  the  most  so,  of 
that  remarkable  group  of  scientific  investigators  who,  in  the  reign  of  Charles  II., 
raised  England  to  the  foremost  place  among  European  nations  in  the  pursuit  of 
ecience,  and  gave  their  period  a  renown  which  has  caused  it  to  be  often  spoken  of, 
and  very  justly,  as  the  classical  age  of  English  science.  .  .  .  Boyle  had  been  since 
1646  engaged  in  chemical  researches  in  London,  being  then  connected  with  the  earlier 


NATURAL  SCIENCE  IN  SEVENTEENTH  CENTURY    261 

markable  little  book  Boyle  by  means  of  a  dialogue  discusses  and 
sharply  criticises  the  chemistry  of  the  "hermetick"  (i.e.  Aris- 
totelian) natural  philosophers,  and  also  "the  vulgar  Spagyrists" 
(i.e.  the  medico-chemists  of  the  Paracelsus  type)  and  questions 
the  value  of  terms  then  hazy  in  their  meaning,  such  as  "element" 
and  "principle,"  as  used  in  alchemy.  He  does  not  himself  pro- 
pound any  new  theories  of  consequence,  but  he  does  insist  on 
more  knowledge,  more  experimentation,  and  less  groundless  specu- 
lation. We  quote  from  Professor  Pattison  Muir's  valuable  intro- 
ductory essay  to  the  "Everyman"  edition :  — 

The  Sceptical  Chymist  embodies  the  reasoned  conceptions  which 
Boyle  had  gained  from  the  experimental  investigations  of  many  physi- 
cal phenomena.  .  .  .  The  book  is  more  than  an  elegant  and  suggestive 
discourse  on  chemico-physical  matters ;  it  is  an  elucidation  of  the  true 
method  of  scientific  inquiry.  ...  At  that  time  the  alchemical  scheme 
of  things  dominated  most  of  those  who  were  inquiring  into  the  trans- 
mutations of  material  substances.  That  scheme  was  based  on  a  magi- 
cal conception  of  the  world.  .  .  .  When  a  magical  theory  of  nature 
prevails,  the  impressions  which  external  events  produce  on  the  senses  of 
observers  are  corrected,  not  by  careful  reasoning  and  accurate  experi- 
mentation, but  by  inquiring  whether  they  fit  into  the  scheme  of  things 
which  has  already  been  elaborated  and  accepted  as  the  truth.  Natural 
events  become  as  clay  in  the  hands  of  the  intellectual  potter  for  whom 
*  there  is  nothing  good  or  bad  but  thinking  makes  it  so/  .  .  .  An  al- 
chemical writer  of  the  seventh  century  said : '  Copper  is  like  a  man ; 
it  has  a  soul  and  a  body/  .  .  .  It  is  not  possible  to  attach  any  definite, 
clear,  meanings  to  alchemical  writings  about  the  four  elements.  Their 
indefiniteness  was  their  strength.  ...  As  the  plain  man  to-day  is 
soothed  and  made  comfortable  by  the  assurance  that  certain  phrases 
to  which  he  attaches  no  definite  meanings  are  really  scientific,  so, 
when  Boyle  lived,  the  plain  man  rested  happily  in  the  belief  that  the 
four  elements  were  the  last  word  of  science  regarding  the  structure  of 
the  materials  of  the  world.  .  .  . 

group  of  scientific  inquirers  in  London  known  as  the  '  Invisible  College '  .  .  .  Boyle, 
too,  we  must  observe,  was  above  all  things  unprejudiced.  He  had  leanings  towards 
alchemy  and  never  quite  repudiated  a  belief  in  the  possibility  of  transmuting  metals. 
In  medical  matters,  which  greatly  interested  him,  he  showed  perfect  tolerance 
towards  those  whom  the  profession  called  quacks.  —  J.  F.  Payne. 


262  A  SHORT  HISTORY  OF  SCIENCE 

Boyle  found  the  same  fault  with  the  'Principles'  of  the  'Vulgar 
Spagyrists '  as  he  found  with  the  '  Elements '  of  the  '  hermetick  philos- 
ophers.' 'Tell  me  what  you  mean  by  your  Principles  and  your  Ele- 
ments,' he  cried;  'then  I  can  discuss  them  with  you  as  working  in- 
struments for  advancing  knowledge.' 

'Methinks  the  Chymists  in  their  search  after  truth  are  not  unlike 
the  navigators  of  Solomon's  Tarshish  Fleet,  who  brought  home  from 
their  long  and  perilous  voyages  not  only  gold  and  silver  and  ivory 
but  apes  and  peacocks  too :  for  so  the  writings  of  several  (I  say  not  all) 
of  your  hermetick  philosophers  present  us,  together  with  diverse  sub- 
stantial and  noble  experiments,  theories  which,  either  like  peacocks' 
feathers,  make  a  great  show,  but  are  neither  solid  nor  useful,  or  else 
like  apes,  if  they  have  some  appearance  of  being  rational,  are  blemished 
with  some  absurdity  or  other  that,  when  they  are  attentively  con- 
sidered, makes  them  appear  ridiculous.' 

The  fact  that  at  the  middle  of  the  seventeenth  century  criticism 
of  this  sort  seemed  to  Boyle  to  be  needed  shows  how  little  real 
progress  toward  modern  scientific  chemistry  had  even  then  been 
made;  and,  as  often  happens,  truth  had  to  be  reached  through 
further  error.  * 

A  FALSE  THEORY  OF  COMBUSTION  :  PHLOGISTON.  —  Two 
German  contemporaries  of  Boyle,  Becher  (1625-1682),  and  Stahl 
(1660-1734),  as  a  result  of  studies  on  combustion  and  the  calcining 
of  metals,  departed  from  the  four  elements  of  antiquity  and 
assumed  the  participation  in  these  processes  of  a  something  dis- 
pelled by  heating.  To  this  something  Stahl  gave  the  name 
phlogiston,  "the  combustible  substance,  a  principle  of  fire,  but  not 
fire  itself."  And  because  from  a  metallic  calx  (oxide)  the  metal 
could  be  recovered  by  burning  with  charcoal,  the  metal  was  held 
to  have  absorbed  "  phlogiston  "  in  the  process  from  the  charcoal, 
which,  having  mostly  disappeared,  was  regarded  as  almost  pure 
phlogiston.  Conversely,  when  the  metal  was  calcined  (or  oxi- 
dized) by  burning  without  charcoal,  it  was  held  to  have  lost  its 
phlogiston.  This  theory,  which  to-day  seems  bizarre,  satisfied 
the  chief  requirement  imposed  on  any  new  theory :  viz.  that  of  ac- 
counting for  the  facts  (as  then  known),  and  was  therefore  naturally 


NATURAL  SCIENCE  IN  SEVENTEENTH  CENTURY    263 

accepted  and  advocated  by  natural  philosophers  for  the  next 
hundred  years.  It  was  not  until  new  facts  had  been  accumulated 
which  were  not  explained  by  the  theory  of  Becher  and  Stahl,  and 
especially  the  fact  revealed  by  the  use  of  the  balance,  that  sub- 
stances calcined  often  gained  weight  (making  it  necessary  to  assume 
that  phlogiston  possessed  negative  gravity,  or  "  levity "  since  its 
loss  increased  weight),  that  the  theory  became  plainly  untenable 
and  was  abandoned.  This,  however,  only  happened  late  in  the 
eighteenth  century,  and  before  this  time  much  progress  had  been 
made  in  chemistry  in  other  directions.  Meanwhile,  in  spite  of  its 
falsity,  the  theory  of  phlogiston  had  done  good  service.  It  had, 
for  example,  effectually  turned  the  attention  of  chemists  away 
from  magic,  from  potable  gold,  and  from  the  making  of  medicines, 
to  speculations  on  composition,  decomposition,  and  chemical 
change,  —  topics  not  only  more  worthy  but  more  fruitful. 

BEGINNINGS  OF  ORGANIC  CHEMISTRY.  —  Meantime,  a  kind  of 
organic  chemistry  was  initiated  by  Hermann  Boerhaave  (1668- 
1738),  a  physician  of  Leyden.  In  the  seventeenth  and  eighteenth 
centuries  the  term  "organic"  stood  more  than  it  does  to-day  for 
the  living  world  and  its  products  which  were  then  regarded  as 
things  altogether  apart  from  the  lifeless  or  inorganic  world.  To- 
day organic  chemistry  hardly  means  more  than  the  chemistry  of 
the  carbon  compounds,  but  at  that  time  it  meant  the  chemistry  of 
bodies  found  in  or  produced  by  living  things.  Medical  men  had 
long  been  interested  in  alchemy,  and  in  more  modern  times  in  iatro- 
chemistry,  so  that  it  was  natural  enough  that  Boerhaave,  a  physi- 
cian, should  undertake  to  subject  organic  substances  to  chemical 
processes.  And  this  he  did,  though  more  in  the  fashion  of  the 
pharmaceutical,  than  the  analytical,  chemist  of  to-day.  Boer- 
haave was  a  famous  teacher  of  medicine  and  of  botany,  and  crowds 
of  students  attended  his  lectures,  thereby  testifying  to  the  now 
rapidly  growing  popularity  of  scientific  learning.  His  Elements 
of  Chemistry,  published  in  1732,  was  widely  used  and  marks  an 
epoch  in  the  history  of  chemistry. 

At  about  the  same  time,  Dr.  Stephen  Hales  (1677-1761),  an 
English  clergyman  of  a  strongly  scientific  bent,  did  similar  work 


264  A  SHORT  HISTORY  OF  SCIENCE 

in  England.  In  addition,  Hales  made  important  studies  on  the 
atmosphere,  and  invented  the  manometer,  which  he  applied  to  the 
measurement  of  the  arterial  blood  pressure  in  the  horse,  and  the 
upward  root  pressure  in  plants,  besides  accomplishing  much  other 
good  work.  Hales  will  perhaps  be  longest  remembered  in  chem- 
istry for  his  skilful  use  of  the  pneumatic  trough,  a  simple  but  in- 
dispensable laboratory  appliance  for  the  easy  collection  of  gases 
in  a  closed  vessel  over  water,  and  especially  for  his  studies  on  air. 

MEDICAL  SCIENCE  AND  MEDICAL  THEORY  IN  THE  SEVENTEENTH 
CENTURY.  THOMAS  SYDENHAM.  —  In  the  middle  of  the  seven- 
teenth century  medical  theory  took  a  long  step  forward  under 
the  influence  of  Thomas  Sydenham  (1624-1689),  often  called  "the 
English  Hippocrates"  because  of  the  naturalism  and  rationalism 
which  he  urged  in  medicine  and  because  of  the  sanity  of  his  opinions 
and  theories.  Setting  aside  magic,  mysticism,  and  the  medical 
chemistry  of  Paracelsus,  and  insisting  on  a  material  basis  (materies 
morbi)  for  the  causes  of  disease,  Sydenham  laid  the  foundations 
of  modern  scientific  medical  philosophy  and  practice.  He  was  a 
close  friend  of  Locke,  the  philosopher,  —  by  whose  materialistic 
and  rationalistic  ideas  he  was  doubtless  influenced,  —  and  was 
also  a  correspondent  of  Boyle.  His  famous  definition  of  disease 
as,  "  An  effort  of  nature,  striving  with  all  her  might  to  restore  the 
patient  by  the  elimination  of  morbific  matter,"  is  still  interesting 
for  its  implication  of  the  modern  idea  of  disease  as  a  struggle  for 
existence  between  pathogenic  matters  (such  as  microbes)  and  the 
inner  forces  of  the  body. 

It  is,  however,  to  Vesalius  and  Harvey,  to  Leeuwenhoek  and 
Kircher  and  Malpighi  and  the  other  microscopists  of  the  seven- 
teenth century,  and  their  successors,  i.e.  to  the  experimenters  and 
laboratory  workers,  rather  than  to  Sydenham  or  his  successors, 
that  medical  science  is  chiefly  indebted,  since  no  great  progress 
could  be  made  in  sound  medical  theory  or  rational  medical  prac- 
tice until  anatomy,  physiology  and  microscopy  had  paved  the 
way  for  a  more  scientific  pathology. 

THE  BEGINNING  OF  MODERN  IDEAS  OP  LIGHT  AND  OPTICS.  — 
The  nature  of  light,  darkness  and  vision  are  very  old  problems. 


NATURAL   SCIENCE   IN   SEVENTEENTH   CENTURY     265 

It  is  easy,  even  for  savages,  to  account  for  daylight  as  sunlight, 
and  the  corresponding  nightlight  as  moonlight  and  starlight,  but 
for  more  highly  developed  man  to  explain  just  what  the  light  is 
which  comes  from  sun,  moon  and  stars,  is  not  so  easy.  Obviously, 
since  "  luminaries  "  —  sun,  moon,  stars,  firebrands  and  torches  — 
produce  light  which  is  weaker  as  distance  from  the  source  in- 
creases, a  kind  of  "emission"  theory  of  light  is  natural  and  reason- 
able. It  was  even  held  by  the  ancients  that  we  see  by  means  of 
light  emitted  from  our  own  eyes,  and  that  light  is  a  more  or  less 
palpable  substance.  A  similar  error  was  held  concerning  heat, 
which  until  the  end  of  the  eighteenth  century  was  generally  re- 
garded as  a  peculiar  material  body  or  substance,  "  caloric,"  which 
when  absorbed  from  other  bodies  produced  a  state  of  heat,  and 
when  emitted  caused,  by  its  absence,  cold. 

How  men  could  have  believed  for  ages  that  objects  are  rendered 
visible  by  something  projected  from  the  eye  itself  —  so  that  the  organ 
of  sight  was  supposed  to  be  analogous  to  the  tentacula  of  insects,  and 
sight  itself  a  mere  species  of  touch  —  is  most  puzzling.  They  seem 
not  till  about  350  B.C.  to  have  even  raised  the  question :  If  this  is  how 
we  see,  Why  cannot  we  see  in  the  dark?  or,  more  simply;  What  is 
darkness?  The  former  of  these  questions  seems  to  have  been  first 
put  by  Aristotle. 

The  ancients  probably  understood  that  light  travels  in  straight 
lines,  and  they  must  have  known  something  about  reflection  and 
refraction  of  light,  for  they  knew  about  images  in  still  water,  and- 
had  mirrors  of  polished  metal,  and  burning  glasses  of  spherical 
glass  shells,  or  balls  of  rock  crystal.  To  Hero  of  Alexandria  we  owe 
the  important  deduction  from  the  Greek  geometers  that  the  course 
of  a  reflected  ray  is  the  shortest  possible  (p.  123). 

The  perfection  of  gem  cutting  among  the  ancients  has  also  been 
held  to  prove  their  acquaintance  with  lenses.  But  it  was  not 
until  the  seventeenth  century  that  modern  ideas  of  light  and 
optics  began  to  be  formulated,  with  the  work  of  Snellius,  Descartes 
and  Newton  on  reflection  and  refraction,  and  of  Romer  on  the 
velocity,  of  light. 


266  A  SHORT  HISTORY  OF  SCIENCE 

Every  student  should  read  the  earlier  parts  of  Newton's  Optics  in 
which  are  described  the  fundamental  experiments  on  the  decomposi- 
tion of  white  light.  —  LORD  RAYLEIGH. 

The  work  of  Christian  Huygens,  towards  the  end  of  the  seven- 
teenth century,  second  only  to  that  of  Newton,  both  hi  extent  and 
importance,  touched  upon  a  great  variety  of  subjects,  including 
some  in  the  natural  sciences.  As  a  young  man  he  wrote  upon 
geometry ;  in  early  middle  life  he  invented  the  cycloidal  pendu- 
lum. He  was  the  first  to  apply  pendulums  to  clocks  and  spiral 
springs  to  watches,  and  to  devise  the  achromatic  eye-piece  which 
still  bears  his  name.  He  also  made  a  telescope  and,  finally,  at 
the  age  of  fifty,  observed  the  phenomena  of  polarization  and, 
most  important  of  all,  proposed  the  modern  wave  theory  of  light. 

THE  FIRST  SCIENTIFIC  INSTRUMENTS:  TELESCOPE,  BAROM- 
ETER, THERMOMETER,  AIR- PUMP,  MICROSCOPE,  MANOMETER. — 
The  complete  history  of  the  origin  of  the  telescope,  the  ther- 
mometer and  the  microscope  is  not  known.  The  account  usually 
given  of  the  invention  of  the  telescope  makes  it  accidental  and 
due  to  the  children  of  a  Dutch  spectacle  maker,  named  Jan  sen, 
who  while  at  play  happened  to  bring  together  two  lenses  in  such 
a  way  that  a  distant  church  spire  seen  through  them  looked  mag- 
nified and  near.  The  father,  whose  attention  was  drawn  to  the 
phenomenon,  seeing  in  the  arrangement  a  source  of  profit,  there- 
upon made  and  sold  the  combination  as  a  toy  or  "wonder,"  under 
, which  form  it  was  on  sale  in  1609,  becoming  known  to  Galileo,  who 
instantly  realized  its  importance  and  made  improvements  in  it.  It 
appears  that  soon  after  1609  Galileo  had  a  fairly  good  instrument, 
magnifying  8  diameters,  with  which  he  was  quickly  and  easily 
able  to  make  some  of  his  most  splendid  astronomical  discoveries. 

The  early  history  of  the  telescope  shows  that  the  effect  of  com- 
bining two  lenses  was  understood  by  scientists  long  before  any  partic- 
ular use  was  made  of  this  knowledge;  and  that  those  who  are 
accredited  with  introducing  perspective  glasses  to  the  public  hit  by 
accident  upon  the  invention.  Priority  was  claimed  by  two  firms  of 
spectacle-makers  in  Middelburg,  Holland,  namely  Zacharias,  miscalled 


PHYSICAL  SCIENCE  IN  SEVENTEENTH  CENTURY     267 

Jansen,  and  Lippershey.  Galileo  heard  of  the  contrivance  in  July 
1609  and  soon  furnished  so  powerful  an  instrument  of  discovery  that 
...  he  was  able  to  make  out  the  mountains  in  the  moon,  the  satel- 
lites of  Jupiter  in  rotation,  the  spots  on  the  revolving  sun  .  .  . 

About  1639,  Gascoigne,  a  young  Englishman,  invented  the  mi- 
crometer which  enables  an  observer  to  adjust  a  telescope  with  very 
great  precision. 

The  history  of  the  microscope  is  closely  connected  with  that  of 
the  telescope.  In  the  first  half  of  the  seventeenth  century  the  simple 
microscope  came  into  use.  It  was  developed  from  the  convex  lens 
.  .  .  Leeuwenhoek  before  1673  had  studied  the  structure  of  minute 
animal  organisms  and  ten  years  later  had  even  obtained  sight  of  bac- 
teria. Very  early  in  the  same  century  Zacharias  had  presented 
Prince  Maurice,  the  commander  of  the  Dutch  forces,  and  the  Arch- 
duke Albert,  Governor  of  Holland,  with  compound  microscopes. 
Kircher  (1601-1680)  made  use  of  an  instrument  that  represented 
microscopic  forms  at  one  thousand  times  larger  than  their  actual 
size.  —  LIBBY.  Introduction  to  the  History  of  Science. 

The  name  of  Galileo  goes  also  with  the  invention  of  the  ther- 
mometer, an  air,  or  more  strictly  a  water,  thermometer  having 
been  introduced  by  him  about  1597.  Mercury  was  not  substituted 
for  water  until  1670,  but  alcohol  thermometers,  also  introduced  by 
Galileo,  were  used  much  earlier.  The  freezing  and  boiling  of 
water  were  supposed  to  take  place  at  variable  temperatures  and 
it  was  not  until  the  end  of  the  seventeenth  century  that  it  was 
realized  that  the  freezing  and  the  boiling  points  are  invariable. 
(For  Galileo's  other  work  in  physics,  see  pp.  246-250.)  Pendulum 
clocks,  "  aerial "  telescopes  and  the  achromatic  eye-pieces  which 
bear  his  name  were  introduced  by  Huygens,  the  first  in  1657 
and  the  others  about  1680.  ^ 

The  invention  of  the  barometer  by  Torricelli  has  already  been 
described  above  (p.  257).  The  air-pump,  though  merely  the  appli- 
cation of  an  ordinary  pump  to  air  instead  of  water,  was  so  rich 
in  its  results  that  it  deserves  a  high  place  among  the  other  and 
more  important  inventions  of  this  remarkable  scientific  era. 

About  the  origin  of  the  (compound)  microscope  there  is  much 


268  A  SHORT  HISTORY  OF  SCIENCE 

the  same  obscurity  as  about  that  of  the  telescope.  Simple  micro- 
scopes such  as  "  magnifiers,"  burning  glasses,  spectacles,  and  other 
lenses,  had  long  been  known,  —  some  of  them  from  antiquity,  — 
but  the  compound  microscope,  which  consists  of  two  lenses  or 
combinations  of  lenses  so  placed  as  to  cooperate  in  the  produc- 
tion of  one  highly  magnified  image  of  a  near  and  minute  object  (the 
telescope  doing  the  same  for  large  and  distant  objects),  first  ap- 
pears about  1650.  Some  of  the  earliest  microscopists  are  Kircher, 
Leeuwenhoek,  Malpighi,  and  Grew.  The  two  former  apparently 
saw  with  the  microscope  and  made  drawings  of  bacteria,  besides 
many  other  micro-organisms  and  cellular  structures.  The  two 
latter  are  the  founders  of  microscopic  anatomy,  Malpighi  of  that 
of  animals,  Grew  of  that  of  plants.  Malpighi's  work  is  especially 
notable,  since  he  for  the  first  time  actually  observed  the  passage  of 
blood  cells  from  arteries  to  veins,  and  that  in  1661  only  four  years 
after  Harvey's  death.  Malpighi's  nam,e  is  also  familiar  to  students 
of  human  anatomy  and  physiology  in  connection  with  those  parts 
of  the  kidneys  and  the  spleen  which  bear  his  name.  The  versatile 
and  accomplished  Englishman  Dr.  Robert  Hooke  (1635-1703),  who 
flourished  in  this  century  and  did  ingenious,  extensive,  and  often 
remarkable  work  at  the  basis  of  almost  every  branch  of  modern 
science,  was  the  first  to  discover  by  the  microscope  the  cellular 
structure  of  living  things.  Hooke  was  one  of  the  original  members 
of  the  Royal  Society,with  which  Leeuwenhoek  also  corresponded. 

The  most  remarkable  fact  connected  with  the  invention  of  the 
compound  microscope  is  that,  because  of  its  physical  imperfec- 
tions, and  in  spite  of  some  use  as  just  described,  it  was  virtually 
abandoned  for  almost  a  century  and  a  half,  and  only  re-introduced 
after  the  invention  and  perfection  of  the  achromatic  objective  in  the 
first  quarter  of  the  nineteenth  century.  The  truth  appears  to  be 
that  owing  to  excessive  spherical  and  chromatic  aberration  the 
compound  microscope  of  the  seventeenth  and  eighteenth  centuries 
was  of  limited  value,  and  that  microscopists  often  preferred  the 
less  powerful,  but  more  perfect,  simple  microscope. 

The  manometer  was  apparently  first  used  by  Stephen  Hales, 
who  measured  with  it  the  blood  pressure  of  a  horse,  the  root  pres- 


PHYSICAL  SCIENCE  IN  SEVENTEENTH  CENTURY    269 

sure  of  plants,  etc.  It  is  described  in  his  Statical  Essays  (1727) 
and  Haemostaticks  (1733). 

ORGANIZATION  OF  THE  FIRST  SCIENTIFIC  ACADEMIES  AND  SO- 
CIETIES.—  The  Academy  of  Plato  (fifth  century  B.C.),  and  the 
Lyceum  of  Aristotle,  the  Museum  at  Alexandria  (third  century  B.C.), 
and  the  so-called  Academy  of  Alcuin  (in  the  eighth  century  A.D.) 
may  be  regarded  as  precursors  of  the  academies  and  societies  of 
the  Renaissance,  but  —  with  the  possible  exception  of  an  academy 
formed  by  Leonardo  da  Vinci  in  the  fifteenth  century  —  the  first 
devoted  chiefly  to  science  was  probably  that  founded  by  della 
Porta  at  Naples  in  1560  and  named  Academia  Secretorum  Naturae. 
The  requirement  for  membership  was  to  have  made  some  dis- 
covery in  natural  science.  Delia  Porta  fell  under  ecclesiastical 
suspicion  as  a  practitioner  of  the  black  arts,  and  though  acquitted 
was  ordered  to  close  his  "Academy."  The  Accademia  del  Lincei 
(of  the  Lynx),  founded  at  Rome  in  1603,  included  both  della  Porta 
and  Galileo  among  its  early  members,  and  still  flourishes.  Its  de- 
vice is  a  lynx  with  upturned  eyes. 

The  Royal  Society  of  London,  like  many  other  societies,  was  the 
outgrowth  of  meetings  of  friends  for  discussion  and  was  chartered 
in  1662.  (For  Boyle's  Invisible  College  see  above,  p.  261.) 

Among  the  earlier  members  of  the  Royal  Society  were  Boyle 
and  Hooke,  Mayow,  Huygens,  Ray,  Grew,  Malpighi,  Leeuwen- 
hoek,  and  Isaac  Newton.  A  well-known  passage  quoted  by 
Huxley  from  Dr.  Wallis,  one  of  the  first  members,  is  of  special 
interest  since  it  shows  what  subjects  were  most  dwelt  upon  by  men 
of  science  at  the  time  of  Cromwell  and  the  Restoration : — 

Some  twenty  years  before  the  outbreak  of  the  plague  (1665),  says 
Huxley,  a  few  calm  and  thoughtful  students  banded  themselves  to- 
gether for  the  purpose,  as  they  phrased  it,  of  *  improving  natural 
knowledge. '  The  ends  they  proposed  to  attain  cannot  be  stated  more 
clearly  than  in  the  words  of  one  of  the  founders  of  the  organisation :  — 

'Our  business  was  (precluding  matters  of  theology  and  state  affairs) 
to  discourse  and  consider  of  philosophical  enquiries,  and  such  as  re- 
lated thereunto :  —  as  Physick,  Anatomy,  Geometry,  Astronomy, 
Navigation,  Staticks,  Magneticks,  Chymicks,  Mechanicks,  and 


270  A  SHORT  HISTORY  OF  SCIENCE 

Natural  Experiments ;  with  the  state  of  these  studies  and  their  cultiva- 
tion at  home  and  abroad.  We  then  discoursed  of  the  circulation  of  the 
blood,  the  valves  in  the  veins,  the  venae  lactece,  the  lymphatic  vessels, 
the  Copernican  hypothesis,  the  nature  of  comets  and  new  stars,  the 
satellites  of  Jupiter,  the  oval  shape  (as  it  then  appeared)  of  Saturn, 
the  spots  on  the  sun  and  its  turning  on  its  own  axis,  the  inequalities 
and  selenography  of  the  moon,  the  several  phases  of  Venus  and  Mer- 
cury, the  improvement  of  telescopes  and  grinding  of  glasses  for  that 
purpose,  the  weight  of  air,  the  possibility  or  impossibility  of  vacuities 
and  nature's  abhorrence  thereof,  the  Torricellian  experiment  in  quick- 
silver, the  descent  of  heavy  bodies  and  the  degree  of  acceleration 
therein,  with  divers  other  things  of  like  nature,  some  of  which  were 
then  but  new  discoveries,  and  others  not  so  generally  known  and  em- 
braced as  now  they  are ;  with  other  things  appertaining  to  what  hath 
been  called  the  New  Philosophy,  which  from  the  times  of  Galileo  *at 
Florence,  and  Sir  Francis  Bacon  (Lord  Verulam)  in  England,  hath 
been  much  cultivated  in  Italy,  France,  Germany,  and  other  parts 
abroad,  as  well  as  with  us  in  England.' 

The  learned  Dr.  Wallis,  writing  in  1696,  narrates  in  these  words 
what  happened  half  a  century  before,  or  about  1645. 

Among  the  first  publications  of  the  Royal  Society  of  London 
were  the  works  of  Malpighi,  the  Italian  microscopical  anatomist, 
in  1669,  and  others  by  Leeuwenhoek,  the  Dutch  microscopist. 

The  French  Academy  (Academic  des  sciences)  began  its  meetings 
in  1666,  and  the  corresponding  Berlin  Academy  in  1700. 

The  oldest  American  association  for  the  promotion  of  science 
is  the  American  Philosophical  Society  Held  at  Philadelphia  for 
Promoting  Useful  Knowledge,  proposed  by  Benjamin  Franklin 
in  1743  and  finally  organized  in  1769.  Franklin  himself  presided 
over  it  from  1769  until  his  death  in  1790. 

THE  NEW  PHILOSOPHY:  BACON  AND  DESCARTES. — It  has  been 
shown  above  how  the  all-inclusive  philosophy  of  their  predecessors 
began  with  Plato  and  Aristotle  to  be  divisible  into  general  and 
"  natural "  philosophy,  —  a  differentiation  which  continued  to 
exist  and  to  increase  slowly  through  the  Middle  Ages  and  the 
Renaissance. 

We  have  also  shown  how  the  mariner's  compass,  the  invention 


BACON   AND    DESCARTES  271 

of  printing,  the  discovery  of  the  New  World,  the  heliocentric 
hypothesis,  the  idea  of  the  earth  as  a  magnet,  the  exploration  of 
the  human  body,  the  Reformation,  and  the  progress  of  mathe- 
matical science,  were  already  widely  opening  men's  minds,  so  that 
by  the  end  of  the  sixteenth  century  it  is  not  surprising  to  find 
the  new  knowledge  reacting  upon  the  old  philosophy.  With  this 
movement  two  great  names  will  always  be  associated  :  viz.  those 
of  Francis  Bacon  and  Rene  Descartes. 

Bacon,  because  of  his  official  position  and  immense  philosophical 
and  literary  ability,  was  able  to  draw  universal  attention  to  the 
methods  of  science  and  especially  to  the  method  of  investigation 
bv  induction,  so  that  his  indirect  service  to  science  was  great. 
Bacon's  true  place  in  science  was,  however,  well  understood  by 
his  contemporaries,  for  one  of  the  greatest,  Harvey,  discoverer  of 
the  circulation  of  the  blood,  remarks  that,  "the  Lord  Chancellor 
writes  of  science  like  —  a  Lord  Chancellor." 

Descartes,  far  more  important  than  Bacon  in  respect  to  his  con- 
tributions to  various  branches  of  science,  likewise  stirred  the  in- 
tellect of  Europe  and  helped  to  bring  about  those  changes  in  the 
old  philosophy  which  in  the  minds  of  many  made  it  new.  Des- 
cartes was  not  only  a  mathematician  of  the  first  rank  but  an  in- 
genious and  original  worker  in  many  branches  of  scientific  inquiry 
such  as  music,  anatomy,  physiology,  optics,  etc.  It  is  to  him  that 
we  owe  the  first  ideas  of  mechanism  in  living  bodies,  his  notion 
of  a  "man  machine"  being  highly  original  and  suggestive. 

Science,  says  Descartes,  may  be  compared  to  a  tree ;  metaphysics 
is  the  root,  physics  the  trunk,  and  the  three  chief  branches  are 
mechanics,  medicine,  and  morals. 

Here  are  my  books,  he  is  reported  to  have  told  a  visitor,  as  he 
pointed  to  the  animals  which  he  had  dissected. 

The  conservation  of  health,  he  writes  in  1646,  has  always  been  the 
principal  end  of  my  studies. 

Bacon  and  Descartes  were  methodologists,  both  urging  the 
fundamental  importance  to  progress,  of  method  and  its  right  use  in 
investigation  and  inquiry,  and  Descartes,  younger  by  almost  a 


272  A  SHORT  HISTORY  OF  SCIENCE 

generation,  admired  and  to  some  extent  imitated  his  predecessor 
in  this  direction. 

PROGRESS  OF  NATURAL  AND  PHYSICAL  SCIENCE  IN  THE 
SEVENTEENTH  CENTURY.  —  A  mere  glance  at  the  Tabular  View 
of  Chronology  in  the  Appendix  will  suffice  to  show  the  immense 
superiority  of  the  seventeenth  to  any  preceding  century  in  the 
number  as  well  as  the  productivity  of  the  workers  devoted  to  the 
mathematical,  and  likewise  to  the  natural  and  physical,  sciences. 
The  achievements  of  this  century  in  natural  philosophy  are 
especially  notable  both  for  their  fundamental  character  and  their 
wide  range.  A  century  which  began  with  a  Galileo  and  ended  with 
a  Huygens  and  a  Newton;  which  witnessed  the  introduction  of 
the  telescope,  the  barometer,  the  thermometer,  the  air-pump,  the 
manometer,  and  the  microscope,  as  well  as  the  organization  of 
the  greatest  and  most  useful  scientific  societies  the  world  has 
hitherto  known,  must  be  forever  famous.  And  when  to  the  names 
and  works  of  Galileo  and  Huygens  and  Newton  we  add  those  of 
Kepler,  Harvey,  Torricelli,  Halley,  Descartes,  Boyle,  Hales, 
Boerhaave,  Leeuwenhoek,  and  Malpighi,  we  have  a  brilliant  com- 
pany indeed. 

REFERENCES  FOR  READING 

FRANCIS  BACON.    Essay  in  Great  Englishmen  of  the  Sixteenth  Century,  by 

Sidney  Lee. 

ROBERT  BOYLE.    Sceptical  Chymist.     (Everyman's  Library.) 
BREWSTER'S  Life  of  Newton,  and  Lives  of  Eminent  Persons. 
R.  DESCARTES.    Life,  by  Haldane. 
R.  DESCARTES,  Discourse  touching  the  method  of  using  one's  reason  rightly 

and  of  seeking  scientific  truth.     Cf.  HUXLEY.    Methods  and  Results,  1896. 
G.  E.  HALE.     National  Academies  and  the  Progress  of  Research. 
WILLIAM  HARVEY  On  The  Movement  of  the  Heart  and  the  Blood.    (Everyman's 

Library.) 

WILLIAM  HARVEY.    By  D'Arcy  Power.    (Masters  of  Medicine  Series.) 
HERSCHEL'S  Familiar  Lectures. 
THOMAS  SYDENHAM.    By  J.  F.  Payne.    (Masters  of  Medicine  Series.) 


CHAPTER  XIII 
BEGINNINGS   OF   MODERN   MATHEMATICAL   SCIENCE 

....  All  the  sciences  which  have  for  their  end  investigations 
concerning  order  and  measure,  are  related  to  mathematics,  it  being 
of  small  importance  whether  this  measure  be  sought  in  numbers,  forms, 
stars,  sounds,  or  any  other  object ;  that,  accordingly,  there  ought  to 
exist  a  general  science  which  should  explain  all  that  can  be  known  about 
order  and  measure,  considered  independently  of  any  application  to  a 
particular  subject,  and  that,  indeed,  this  science  has  its  own  proper 
name,  consecrated  by  long  usage,  to  wit,  mathematics.  And  a  proof 
that  it  far  surpasses  in  facility  and  importance  the  sciences  which  de- 
pend upon  it  is  that  it  embraces  at  once  all  the  objects  to  which  these 
are  devoted  and  a  great  many  others  besides.  ...  —  Descartes. 

As  long  as  algebra  and  geometry  proceeded  along  separate  paths, 
their  advance  was  slow  and  their  applications  limited.  But  when 
these  sciences  joined  company,  they  drew  from  each  other  fresh  vitality 
and  thenceforward  marched  on  at  a  rapid  pace  toward  perfection. 

—  Lagrange. 

The  application  of  algebra  has  far  more  than  any  of  his  meta- 
physical speculations,  immortalized  the  name  of  Descartes,  and  con- 
stitutes the  greatest  single  step  ever  made  in  the  progress  of  the 
exact  sciences.  —  Mill. 

The  idea  of  coordinates  which  forms  the  indispensable  scheme  for 
making  all  processes  visible,  with  its  many-sided  and  stimulating 
applications  in  all  branches  of  daily  life,  —  whether  medicine,  physi- 
cal geography,  political  economy,  statistics,  insurance,  the  technical 
sciences  —  the  first  beginnings  of  the  calculus  in  their  historical 
evolution,  the  development  of  the  ideas  of  function  and  limit  in 
connection  with  the  elementary  theory  of  curves,  these  are  things 
without  which  in  the  present  day  not  the  slightest  comprehension  of 
the  phenomena  of  nature  can  be  attained,  of  which,  however,  the 
knowledge  enables  us  as  by  magic  to  gain  an  insight  with  which  in 
depth  and  range,  but  above  all  in  certainty,  scarcely  any  other  can  be 
compared.  —  Voss. 

How  many  celebrate  the  names  of  Newton  and  Leibnitz  !  How  few 
have  a  real  appreciation  of  that  which  these  men  have  created  of 
permanent  value  !  Here  lie  the  roots  of  our  present-day  knowledge, 
here  the  true  continuation  of  the  strivings  of  antique  wisdom. 

—  Lindemann. 
T  273 


274  A  SHORT  HISTORY  OF  SCIENCE 

The  invention  of  the  differential  calculus  marks  a  crisis  in  the 
history  of  mathematics.  The  progress  of  science  is  divided  between 
periods  characterized  by  a  slow  accumulation  of  ideas  and  periods, 
when,  owing  to  the  new  material  for  thought  thus  patiently  collected, 
some  genius  by  the  invention  of  a  new  method  or  a  new  point  of 
view,  suddenly  transforms  the  whole  subject  on  to  a  high  level. 

—  Whitehead. 

MATHEMATICAL  PHILOSOPHY.  ANALYTIC  GEOMETRY.  DES- 
CARTES. — The  invention  of  analytic  geometry  by  Descartes  in  1637 
and  the  almost  contemporary  introduction  of  integral  calculus  as 
the  method  of  "  indivisibles"  may  be  regarded  as  the  real  beginning 
of  modern  mathematical  science.  Thanks  to  these  fruitful  ideas 
the  science  has  during  the  three  centuries  that  have  since  elapsed 
made  extraordinary  progress  both  in  its  own  internal  development 
and  in  its  application  throughout  the  range  of  the  physical  sciences. 

Descartes  was  born  in  Touraine  in  1596,  and  after  the  education 
appropriate  for  a  youth  of  family  and  some  years  of  fashionable 
life  in  Paris,  entered  the  army,  then  in  Holland.  His  military 
career  continued  till  1621  with  incidental  opportunity  for  his 
favorite  speculations  in  mathematics  and  philosophy.  Some  of 
his  most  fruitful  ideas  dated  from  dreams  and  his  best  thinking 
was  habitually  done  before  rising. 

It  is  impossible  not  to  feel  stirred  at  the  thought  of  the  emotions 
of  men  at  certain  historic  moments  of  adventure  and  discovery  — 
Columbus  when  he  first  saw  the  Western  shore,  Franklin  when  the 
electric  spark  came  from  the  string  of  his  kite,  Galileo  when  he  first 
turned  his  telescope  to  the  heavens.  Such  moments  are  also  granted 
to  students  in  the  abstract  regions  of  thought,  and  high  among  them 
must  be  placed  the  morning  when  Descartes  lay  in  bed  and  invented 
the  method  of  coordinate  geometry.  —  Whitehead. 

In  order  to  devote  himself  more  completely  to  his  favorite 
studies  he  settled  in  Holland  in  1629,  devoting  the  next  four  years 
to  writing  a  treatise,  entitled  Le  Monde,  upon  the  universe.  In  1637 
he  published  his  great  Discourse  on  the  Method  of  Good  Reasoning 
and  of  Seeking  Truth  in  Science.1  This  begins :  — 

1  Discours  de  la  Methode  pour  bien  conduire  sa  raison  et  chercher  la  verite  dans 
les  sciences. 


BEGINNINGS  OF  MODERN  MATHEMATICAL  SCIENCE    275 

If  this  discourse  seems  too  long  to  be  read  all  at  once,  it  can  be 
divided  into  six  parts.  In  the  first  will  be  found  various  considera- 
tions concerning  the  sciences ;  in  the  second,  the  chief  rules  of  the 
method  which  the  author  has  sought;  in  the  third,  some  of  those 
of  ethics  which  he  has  deduced  by  this  method ;  in  the  fourth,  the 
reasons  by  which  he  proves  the  existence  of  God  and  of  the  human 
soul,  which  are  the  foundations  of  his  metaphysics ;  in  the  fifth,  the 
order  of  questions  of  physics  which  he  has  sought,  and  particularly 
the  explanation  of  the  movement  of  the  heart  and  of  some  other 
difficulties  which  belong  to  medicine ;  also  the  difference  which  exists 
between  our  soul  and  that  of  the  beasts;  and  in  the  last,  what 
things  he  believes  necessary  in  order  to  go  farther  in  the  investiga- 
tion of  nature  than  has  been  done,  and  what  reasons  have  made 
him  write. 

Good  sense  is  the  most  widely  distributed  commodity  in  the 
world,  for  every  one  thinks  himself  so  well  supplied  with  it  that  even 
those  who  are  hardest  to  satisfy  in  every  other  respect  are  not  accus- 
tomed to  desire  more  of  it  than  they  have.  In  this  it  is  not  prob- 
able that  all  men  are  mistaken,  but  rather  this  testifies  that  the  power 
of  good  judgment  and  of  discriminating  between  the  true  and  the  false, 
which  is  properly  what  one  calls  good-sense  or  reason,  is  naturally 
equal  in  all  men ;  and  thus  that  the  diversity  of  our  opinions  is  not 
due  to  the  fact  that  some  are  more  reasonable  than  others,  but  only 
that  we  conduct  our  thought  along  different  channels,  and  do  not 
consider  the  same  things.  For  it  is  not  enough  to  have  a  good  mind, 
but  the  principal  thing  is  to  apply  it  well.  The  greatest  souls  are 
capable  of  the  greatest  vices  as  well  as  of  the  greatest  virtues :  and 
those  who  only  progress  very  slowly  can  advance  much  more,  if 
they  follow  always  the  straight  road  than  do  those  who  run,  depart- 
ing from  it. 

His  four  cardinal  precepts  were :  — 

Never  to  receive  anything  for  true  which  he  did  not  recognize  to  be 
evidently  so;  that  is,  to  avoid  carefully  precipitancy  and  prejudg- 
ment.  Second,  to  divide  each  of  the  difficulties  which  he  should 
examine  into  as  many  pieces  as  possible.  Third,  to  conduct  his 
thoughts  in  order,  beginning  with  the  simplest  objects.  The  last, 
to  make  everywhere  enumerations  so  complete  and  reviews  so  general 
that  he  should  be  assured  of  omitting  nothing. 


276  A  SHORT  HISTORY  OF  SCIENCE 

Three  appendices  dealt  with  optics,  meteors,  and  geometry, 
the  last  containing  the  beginnings  of  analytic  geometry.  The 
relation  of  his  philosophy  to  mathematics  may  be  indicated  in 
the  following  passages. 

Considering  that,  among  all  those  who  up  to  this  time  made  dis- 
coveries in  the  sciences,  it  was  the  mathematicians  alone  who  had 
been  able  to  arrive  at  demonstrations  —  that  is  to  say,  at  proofs  cer- 
tain and  evident  —  I  did  not  doubt  that  I  should  begin  with  the  same 
truths  that  they  have  investigated,  although  I  had  looked  for  no  other 
advantage  from  them  than  to  accustom  my  mind  to  nourish  itself  upon 
truths  and  not  to  be  satisfied  with  false  reasons. 

When  ...  I  asked  myself  why  was  it  then  that  the  earliest  phi- 
losophers would  admit  to  the  study  of  wisdom  only  those  who  had 
studied  mathematics,  as  if  this  science  was  the  easiest  of  all  and  the 
one  most  necessary  for  preparing  and  disciplining  the  mind  to  com- 
prehend the  more  advanced,  I  suspected  that  they  had  knowledge 
of  a  mathematical  science  different  from  that  of  our  time.  .  .  . 

I  believe  I  find  some  traces  of  these  true  mathematics  in  Pappus 
and  Diophantus,  who,  although  they  were  not  of  extreme  antiquity, 
lived  nevertheless  in  times  long  preceding  ours.  But  I  willingly  be- 
lieve that  these  writers  themselves,  by  a  culpable  ruse,  suppressed  the 
knowledge  of  them ;  like  some  artisans  who  conceal  their  secret,  they 
feared,  perhaps,  that  the  ease  and  simplicity  of  their  method,  if 
become  popular,  would  diminish  its  importance,  and  they  preferred 
to  make  themselves  admired  by  leaving  to  us,  as  the  product  of 
their  art,  certain  barren  truths  deduced  with  subtlety,  rather  than 
to  teach  us  that  art  itself,  the  knowledge  of  which  would  end  our 
admiration. 

Those  long  chains  of  reasoning,  quite  simple  and  easy,  which  geom- 
eters are  wont  to  employ  in  the  accomplishment  of  their  most  difficult 
demonstrations,  led  me  to  think  that  everything  which  might  fall 
under  the  cognizance  of  the  human  mind  might  be  connected  together 
iin  a  similar  manner,  and  that,  provided  only  that  one  should  take 
•care  not  to  receive  anything  as  true  which  was  not  so,  and  if  one 
were  always  careful  to  preserve  the  order  necessary  for  deducing 
one  truth  from  another,  there  would  be  none  so  remote  at  which 
he  might  not  at  last  arrive,  nor  so  concealed  which  he  might  not 
discover. 


BEGINNINGS  OF  MODERN  MATHEMATICAL  SCIENCE    277 

Descartes  had  attempted  the  solution  of  a  historic  geometrical 
problem  propounded  by  Pappus.  From  a  point  P  perpendiculars 
are  dropped  on  m  given  straight  lines  and  also  on  n  other  given 
lines.  The  product  of  the  m  perpendiculars  is  in  a  constant 
ratio  to  the  product  of  the  n;  it  is  required  to  determine  the  locus 
of  P.  Pappus  had  stated  without  proof  that  for  m  =  n  =  2  the 
locus  is  a  conic  section,  Descartes  showed  this  algebraically,  — 
Newton  afterwards  conquering  the  difficulty  by  unaided  geometry. 

Descartes  distinguished  geometrical  curves  for  which  x  and  y 
may  be  regarded  as  changing  at  commensurable  rates,  or  as  we 
should  say,  curves  for  which  the  slope  is  an  algebraic  function 
of  the  coordinates,  from  curves  which  do  not  satisfy  this  condition. 
These  he  called  "mechanical,"  and  did  not  discuss  further.  For 
the  accepted  definition  of  a  tangent  as  a  line  between  which  and 
the  curve  no  other  line  can  be  drawn,  he  introduced  the  modern 
notion  of  limiting  position  of  a  secant.  In  connection  with  this 
he  considered  a  circle  meeting  the  given  curve  in  two  consecutive 
points,  a  perpendicular  to  the  radius  of  the  circle  being  a  common 
tangent  to  the  circle  and  the  given  curve.  The  circle  was  not 
however  that  of  curvature,  but  had  its  centre  on  an  axis  of  sym- 
metry of  the  given  curve.  He  recognized  the  possibility  of  ex- 
tending his  methods  to  space  of  three  dimensions,  but  did  not  work 
out  the  details.  His  geometry  contained  also  a  discussion  of  the 
algebra  then  known,  and  gave  currency  to  certain  important  inno- 
vations, in  particular  the  systematic  use  of  a,  b,  and  c,  for  known, 
x,  y,  and  z,  for  unknown  quantities ;  the  introduction  of  exponents ; 
the  collection  of  all  terms  of  an  equation  in  one  member ;  the  free 
use  of  negative  quantities ;  the  use  of  undetermined  coefficients  in 
solving  equations ;  and  his  rule  of  signs  for  studying  the  number 
of  positive  or  negative  roots  of  equations.  He  even  fancied  that 
he  had  found  a  method  for  solving  an  equation  of  any  degree. 

It  is  important  to  distinguish  just  what  Descartes  contributed 
to  mathematics  in  his  analytic  geometry.  Neither  the  com- 
bination of  algebra  with  geometry  nor  the  use  of  coordinates  was 
new.  From  the  time  of  Euclid  quadratic  equations  had  been 
solved  geometrically,  while  latitude  and  longitude  involving  a 


278  A  SHORT  HISTORY  OF  SCIENCE 

system  of  coordinates  are  of  similar  antiquity.  The  great  step 
made  by  Descartes  was  his  recognition  of  the  equivalence  of  an 
equation  and  the  geometrical  locus  of  a  point  whose  coordinates 
satisfy  that  equation.  On  this  foundation  facts  known  or  ascer- 
tainable  about  geometry  may  be  translated  into  algebra  and  con- 
versely. The  advantage  is  comparable  with  that  conferred  by  the 
possession  of  two  arms  or  eyes,  or  even  two  senses,  under  a  common 
will.  The  intricate  but  powerful  machinery  of  algebra  becomes 
available  for  solving  geometrical  problems,  while,  on  the  other 
hand,  the  geometrical  illustration  makes  the  algebra  visible  and 
concrete. 

Later  works  dealt  with  philosophy  and  physical  science,  in  par- 
ticular with  a  theory  of  vortices.  Descartes  enunciates  ten 
natural  laws,  the  first  two  corresponding  with  the  first  two  of 
Newton's.  He  argues  that  all  matter  is  in  motion  and  that  this 
must  result  in  the  formation  of  vortices.  The  sun  is  the  centre  of 
one  great  vortex,  each  planet  of  its  own,  thus  approximating 
vaguely  the  future  nebular  hypothesis.  Newton  thought  it  worth 
while  to  refute  this  theory,  which  was  chiefly  notable  as  a  bold 
attempt  to  interpret  the  phenomena  of  the  universe  by  means  of 
a  single  mechanical  principle. 

Lord  Kelvin  has  expressed,  with  all  his  force,  that  the  sole  satis- 
factory explanation  of  the  phenomena  of  nature  is  that  which  leads 
them  back  in  the  last  analysis  to  motion  in  a  continuous  incompres- 
sible fluid.  This  however  was  the  guiding  thought  with  Descartes. 

— Timerding. 

Descartes's  achievements  in  mathematics  leave  no  doubt  of  his 
exceptional  intellectual  power.  He  had  neither  the  data  nor  the 
scientific  method  for  accomplishing  similar  results  in  other  branches 
of  science,  and  in  mathematics  he  would  doubtless  have  accom- 
plished much  more  had  he  not  expended  his  energies  so  widely 
in  over-confident  reliance  on  his  logical  method.  He  died  at 
Stockholm  in  1650. 

INDIVISIBLES.  CAVALIERI.  —  While  Descartes  was  thus  as  it 
were  incidentally  laying  the  foundations  of  modern  geometrical 


BEGINNINGS  OF  MODERN  MATHEMATICAL  SCIENCE    279 

analysis,  his  Italian  contemporary,  Cavalieri  (1598-1647)  was 
rendering  a  similar  service  to  the  integral  calculus  in  developing 
his  theory  of  indivisibles. 

The  problem  of  measuring  the  length  of  a  curve  or  the  area  of 
a  figure  having  a  curved  boundary,  or  the  volume  of  a  solid  bounded 
by  a  curved  surface  goes  back  indeed  to  comparatively  ancient 
Greek  times.  Most  notable  in  this  direction  was  the  work  of 
Archimedes.  Kepler,  attempting  to  resolve  astronomical  difficulties 
by  the  hypothesis  of  elliptical  orbits,  is  confronted  at  once  with 
the  problem  of  determining  the  circumference  of  an  ellipse.  He 
gives  the  approximation  TT  (a  +  6)  where  a  and  b  are  the  semi- 
axes.  This  is  close  if  a  and  b  are  nearly  equal,  as  in  most  of  the 
planetary  orbits.  Interesting  himself  in  current  methods  of 
measuring  the  capacity  of  casks,  he  published  in  1615  his  Nova 
Stereometric,  Doliorum  Vinariorum,  in  which  he  determines  the 
volumes  of  many  solids  bounded  by  surfaces  of  revolution.  The 
Greek  method  had  in  case  of  the  circle,  etc.,  depended  on  an 
"exhaustion"  process  of  inscribing  and  circumscribing  polygons 
differing  less  and  less  from  the  curve  both  in  boundary  and  in 
area.  Kepler  however  divided  his  solid  into  sections,  determined 
the  area  of  a  section  and  then  sought  the  sum.  He  lacked  an 
adequate  system  of  coordinates,  a  clearly  defined  conception  of  a 
limit,  and  an  effective  method  of  summation.  In  view  of  the 
intrinsic  difficulty  of  this  important  problem,  however,  the  extent 
of  his  success  is  remarkable. 

He  also  sought  to  determine  the  most  economical  proportions 
for  casks,  etc.,  expressing  his  view  of  the  underlying  mathematical 
theory  by  the  theorem  "  In  points  where  the  transition  from  a  less 
to  the  greatest  and  again  to  a  less  takes  place,  the  difference  is 
always  to  a  certain  degree  imperceptible." 

Cavalieri,  in  1635,  adopted  the  form  of  statement  that  a  line 
consists  of  an  infinite  number  of  points,  a  surface  of  an  infinity  of 
lines,  a  solid  of  an  infinity  of  surfaces,  but  later  revised  this  on  the 
basis  of  the  assumption  "that  any  magnitude  may  be  divided 
into  an  infinite  number  of  small  quantities  which  can  be  made  to 
bear  any  required  ratios  one  to  the  other."  On  this  basis,  open 


280 


A  SHORT  HISTORY  OF  SCIENCE 


as  it  was  to  criticism,  were  solved  simple  area  problems  involving 
the  parabola  and  the  hyperbola. 

The  principle  of  comparing  areas  by  comparing  lengths  of  a 
system  of  parallel  lines  crossing  them  is  easily  illustrated  in  the 
case  of  the  ellipse  by  comparing  it  with  the  circle  having  as  its 
diameter  the  (horizontal)  major  axis  of  the  ellipse.  If  a  and  b 
are  the  semi-axes  of  the  ellipse  the  two 
curves  are  known  to  be  so  related  that  every 
vertical  chord  of  the  circle  is  in  a  fixed  ratio 
a :  b  to  the  part  of  it  lying  within  the  ellipse. 
The  area  of  the  circle  must  bear  the  same 
relation  to  the  area  of  the  ellipse.  The 
transition  from  length  to  area  while  not 
rigorously  worked  out  by  Cavalieri  does  not 
necessarily  involve  the  false  assumption  that 
area  consists  of  the  sum  of  parallel  lines.  A  similar  method  is 
evidently  applicable  to  volumes.  Thus  was  anticipated  one  of  the 
most  interesting  and  important  processes  of  modern  mathematics, 
—  integration  as  a  summation. 

Similarly  Cavalieri  determined  volumes  by  a  consideration  of 
the  thin  sections  or  elements  into  which  they  may  be  resolved  by 
parallel  planes.  The  principle  that  "two  bodies  have  the  same 
volume  if  sections  at  the  same  level  have  the  same  area"  is  still 
known  by  his  name. 

Descartes's  work  with  tangents  seems  not  to  have  led  him  to 
develop  the  fundamental  ideas  of  the  differential  calculus,  and  it 
appeared  that  the  integral  calculus  would  be  evolved  first  from  the 
work  of  Cavalieri. 

PROJECTIVE  GEOMETRY  :  DESARGUES.  —  Hardly  less  interesting 
than  the  new  ideas  of  Descartes  and  Cavalieri  are  those  of  their 
contemporary  Desargues  (1593-1662),  an  engineer  and  architect 
of  Lyons,  who  made  important  researches  in  geometry.  But  for 
the  still  more  brilliant  geometrical  achievements  of  Descartes, 
these  might  have  led  to  the  immediate  development  of  projective 
geometry,  the  elements  of  which  are  contained  in  Desargues's 
work.  In  general  this  geometry  instead  of  dealing  with  definite 


BEGINNINGS  OF  MODERN  MATHEMATICAL  SCIENCE    281 

triangles,  polygons,  circles,  etc.,  in  the  Euclidean  manner,  is  based 
on  a  consideration  of  all  points  of  a  straight  line,  of  all  lines  through 
a  common  point  and  of  the  possible  effects  of  setting  up  an  orderly 
one-to-one  correspondence  between  them.  In  particular,  Des- 
argues  makes  a  comparative  study  of  the  different  plane  sections 
of  a  given  cone,  deducing  from  known  properties  of  the  circle  anal- 
ogous results  for  the  other  conic  sections. 

In  his  chief  work  Desargues  enunciates  the  propositions :  — 

1.  A  straight  line  can  be  considered  as  produced  to  infinity 
and  then  the  two  opposite  extremities  are  united. 

2.  Parallel  lines  are  lines  meeting  at  infinity  and  conversely. 

3.  A  straight  line  and  a  circle  are  two  varieties  of  the  same 
species. 

On  these  he  bases  a  general  theory  of  the  plane  sections  of  a  cone. 

Desargues  contented  himself  with  enunciating  general  princi- 
ples, remarking :  —  "  He  who  shall  wish  to  disentangle  this  prop- 
osition will  easily  be  able  to  compose  a  volume."  He  met 
Descartes  while  employed  by  Cardinal  Richelieu  at  the  siege  of 
Rochelle,  and  they  with  others  met  regularly  in  Paris  for  the 
discussion  of  the  new  Copernican  theory  and  other  scientific 
problems. 

He  says  '  I  freely  confess  that  I  never  had  taste  for  study  or  re- 
search either  in  physics  or  geometry  except  in  so  far  as  they  could 
serve  as  a  means  of  arriving  at  some  sort  of  knowledge  of  the  proxi- 
mate causes  ....  for  the  good  and  convenience  of  life,  in  maintaining 
health,  in  the  practice  of  some  art, ....  having  observed  that  a  good 
part  of  the  arts  is  based  on  geometry,  among  others  the  cutting  of 
stones  in  architecture,  that  of  sun-dials,  that  of  perspective  in 
particular/ 

Perceiving  that  the  practitioners  of  these  arts  had  to  burden  them- 
selves with  the  laborious  acquisition  of  many  special  facts  in 
geometry,  he  sought  to  relieve  them  by  developing  more  general 
methods  and  printing  notes  for  distribution  among  his  friends. 

An  interesting  theorem  bearing  his  name  and  typical  of  pro- 
jective  geometry  is  as  follows :  —  If  two  triangles  ABC  and  A'B'C' 


282 


A  SHORT  HISTORY  OF  SCIENCE 


are  so  related  that  lines  joining  corresponding  vertices  meet  in  a 
point  O,  then  the  intersections  of  corresponding  sides  will  lie 

in  a  straight  line  A"B"C".  It 
remained  for  Monge,  the  inventor  of 
descriptive  geometry  (p.  335)  and 
others  more  than  a  century  later 
to  carry  this  development  forward. 
Desargues's  work  was  indeed  prac- 
tically lost  until  Poncelet  in  1822 
proclaimed  him  the  Monge  of  his 
century. 

THEORY  OF  NUMBERS  AND  PROBABILITY  :  FERMAT,  PASCAL.  — 
But  little  younger  than  Descartes  and  Cavalieri  was  Pierre  de 
Fermat  (1601-1665)  a  man  of  quite  exceptional  position  in  mathe- 
matical history.  Devoting  to  mathematics  such  leisure  as  his 
public  duties  afforded,  he  nevertheless  published  almost  noth- 
ing, many  of  his  results  being  known  to  us  only  in  the  form  of 
brief  marginal  notes  without  proof.  In  editing  Diophantus  he 
enunciated  numerous  theorems  on  integers,  for  example, 

An  odd  prime  can  be  expressed  as  the  difference  of  two  square 
integers  in  one  and  only  one  way. 

No  integral  values  of  x,  y,  z  can  be  found  to  satisfy  the  equation 
x*  +  yn  =  2">  if  n  be  an  integer  greater  than  2. 

This  seemingly  simple  theorem  has  been  verified  for  so  wide  a 
range  of  values  of  n,  that  its  truth  can  hardly  be  doubted,  but  no 
general  proof  has  yet  been  given  in  spite  of  a  prize  of  100,000  marks 
awaiting  him  who  either  proves  or  disproves  it.  Some  writers  even 
credit  Fermat  with  a  substantial  share  in  the  invention  of  the  new 
analytic  geometry,  in  which  he  had  certainly  done  independent 
work  for  some  years  before  Descartes's  publication.  Laplace  in- 
deed calls  Fermat  "the  true  inventor  of  the  differential  calculus." 
He  discusses  problems  of  maxima  and  minima,  and  passing  to 
concrete  phenomena,  enunciates  the  interesting  theorem :  that 
Nature,  the  great  workman  which  has  no  need  of  our  instru- 
ments and  machines,  lets  everything  happen  with  a  minimum  of 


BEGINNINGS  OF  MODERN  MATHEMATICAL  SCIENCE    283 

outlay,  —  an  idea  not  indeed  strange  to  some  of  the  Greeks. 
The  law  of  refraction  of  a  ray  of  light  he  deals  with  correctly  as 
a  particular  case  of  the  principle  of  economy,  a  principle  which 
exerted  a  potent  influence  in  the  scientific  philosophy  of  the 
following  century.  Thus  for  example  Euler  says  in  1744 :  — 

Since  the  organization  of  the  world  is  the  most  excellent,  nothing  is 
found  in  it,  out  of  which  some  sort  of  a  maximum  or  minimum 
property  does  not  shine  forth.  Therefore  no  doubt  can  exist,  that  all 
action  in  the  world  can  be  derived  by  the  method  of  maxima  and 
minima  as  well  as  from  the  actual  operating  causes. 

Fermat's  work  in  the  theory  of  probability  is  fundamental.  He 
discusses  the  case  of  two  players,  A  and  B,  where  A  wants  two 
points  to  win  and  B  three  points.  Then  the  game  will  certainly 
be  decided  in  the  course  of  four  trials.  Take  the  letters  a  and  b, 
and  write  down  all  the  combinations  that  can  be  formed  of  four 
letters.  These  combinations  are  16  in  number,  namely  aaaa, 
aaab,  aaba,  aabb,  abaa,  abab,  abba,  abbb,  baaa,  baab,  baba,  babb, 
bbaa,  bbab,  bbba,  bbbb.  Now  every  combination  in  which  a  oc- 
curs twice  or  oftener  represents  a  case  favorable  to  A,  and  every 
combination  in  which  b  occurs  three  times  or  oftener  represents  a 
case  favorable  to  B.  Thus,  on  counting  them,  it  will  be  found 
that  there  are  11  cases  favorable  to  A,  and  5  cases  favorable  to 
B ;  and,  since  these  cases  are  all  equally  likely,  A's  chance  of  win- 
ning the  game  is  to  B's  chance  as  11  is  to  5. 

Like  Descartes,  Pascal  (1623-1662)  devoted  but  a  fraction  of 
his  great  talent  to  mathematical  science. 

I  have  spent  much  time  in  the  study  of  the  abstract  sciences,  — 
but  the  paucity  of  persons  with  whom  you  can  communicate  on  such 
subjects  gave  me  a  distaste  for  them.  When  I  began  to  study  man, 
I  saw  that  these  abstract  studies  were  not  suited  to  him,  and  that  in 
diving  into  them,  I  wandered  farther  from  my  real  track  than  those 
who  were  ignorant  of  them,  and  I  forgave  men  for  not  having  at- 
tended to  these  things.  But  I  thought  at  least  I  should  find  many 
companions  in  the  study  of  mankind,  which  is  the  true  and  proper  study 
of  man.  Again  I  was  mistaken.  There  are  yet  fewer  students  of  Man 
than  of  Geometry. 


284  A  SHORT  HISTORY  OF  SCIENCE 

Learning  geometry  surreptitiously  at  12  years,  he  had  at  18 
written  an  essay  on  conic  sections  and  constructed  the  first  com- 
puting machine.  While  most  of  his  later  life  was  devoted  to  re- 
ligion, theology,  and  literature,  he  undertook  a  wide  range  of 
physical  experimentation,  and  made  important  contributions  to 
the  then  new  theories  of  numbers  and  probability,  besides  a 
discussion  of  the  cycloid.  The  juvenile  essay  on  conic  sections 
contains  the  beautiful  theorem  since  named  for  him  that  the 
opposite  sides  of  a  hexagon  inscribed  in  a  conic  section  meet  in  a 
straight  line.  Of  geometry  and  logic  Pascal  says :  — 

Logic  has  borrowed  the  rules  of  geometry  without  understanding 
its  power.  ...  I  am  far  from  placing  logicians  by  the  side  of  geom- 
eters who  teach  the  true  way  to  guide  the  reason.  .  .  .  The  method 
of  avoiding  error  is  sought  by  every  one.  The  logicians  profess  to 
lead  the  way,  the  geometers  alone  reach  it,  and  aside  from  their  science 
there  is  no  true  demonstration. 

His  work  on  probability  connected  itself  with  the  problem  of 
two  players  of  equal  skill  wishing  to  close  their  play,  of  which 
Fermat's  solution  has  been  given  above. 

The  following  is  my  method  for  determining  the  share  of  each 
player  when,  for  example,  two  players  play  a  game  of  three  points 
and  each  player  has  staked  32  pistoles. 

Suppose  that  the  first  player  has  gained  two  points  and  the  second 
player  one  point ;  they  have  now  to  play  for  a  point  on  this  condition, 
that  if  the  first  player  gain,  he  takes  all  the  money  which  is  at  stake, 
namely  64  pistoles ;  while  if  the  second  player  gain,  each  player  has 
two  points,  so  that  they  are  on  terms  of  equality,  and  if  they  leave 
off  playing,  each  ought  to  take  32  pistoles.  Thus  if  the  first  player 
gain,  then  64  pistoles  belong  to  him,  and  if  he  lose,  then  32  pistoles 
belong  to  him.  If  therefore  the  players  do  not  wish  to  play  this  game, 
but  separate  without  playing  it,  the  first  player  would  say  to  the 
second,  '  I  am  certain  of  32  pistoles,  even  if  I  lose  this  point,  and  as 
for  the  other  32  pistoles,  perhaps  I  shall  have  them  and  perhaps  you 
will  have  them ;  the  chances  are  equal.  Let  us  then  divide  these  32 
pistoles  equally,  and  give  me  also  the  32  pistoles  of  which  I  am  certain/ 
Thus  the  first  player  will  have  48  pistoles  and  the  second  16  pistoles. 


BEGINNINGS  OF  MODERN  MATHEMATICAL  SCIENCE    285 

By  similar  reasoning  he  shows  that  if  the  first  player  has  gained 
two  points  and  the  second  none,  the  division  should  be  56  to  8 ; 
while  if  the  first  has  gained  one  point,  the  second  none,  it  should 
be  44  and  20. 

The  calculus  of  probabilities,  when  confined  within  just  limits, 
ought  to  interest,  in  an  equal  degree,  the  mathematician,  the  experi- 
mentalist, and  the  statesman.  From  the  time  when  Pascal  and 
Fermat  established  its  first  principles,  it  has  rendered,  and  continues 
daily  to  render,  services  of  the  most  eminent  kind.  It  is  the  calculus 
of  probabilities,  which,  after  having  suggested  the  best  arrangements 
of  the  tables  of  population  and  mortality,  teaches  us  to  deduce  from 
those  numbers,  in  general  so  erroneously  interpreted,  conclusions  of 
a  precise  and  useful  character ;  it  is  the  calculus  of  probabilities  which 
alone  can  regulate  justly  the  premiums  to  be  paid  for  assurances; 
the  reserve  funds  for  the  disbursements  of  pensions,  annuities,  dis- 
counts, etc.  It  is  under  its  influence  that  lotteries  and  other  shameful 
snares  cunningly  laid  for  avarice  and  ignorance  have  definitely  disap- 
peared. —  Arago. 

With  this  work  connected  itself  his  arithmetical  triangle  in  which 
successive  diagonals  contain  the  coefficients  which  occur  in  ex- 
pansions by  the  binomial  theorem,  which  Newton  was  soon  to 
generalize. 

111111 

12345 

1  3  6  10 

1  4  10 

1  5 

1 

He  applies  the  method  of  indivisibles  successfully  to  the  cycloid 
(the  curve  generated  by  a  point  on  the  rim  of  a  rolling  wheel). 

Pascal  invented  in  1645  an  arithmetical  machine,  writing  the 
Chancellor  in  regard  to  it : 

Sir :  If  the  public  receives  any  advantage  from  the  invention  which 
I  have  made  to  perform  all  sorts  of  rules  of  arithmetic  in  a  manner  as 
novel  as  it  is  convenient,  it  will  be  under  greater  obligation  to  your 


286  A  SHORT  HISTORY  OF  SCIENCE 

Highness  than  to  my  small  efforts,  since  I  should  only  have  been  able 
to  boast  of  having  conceived  it,  while  it  owes  its  birth  absolutely  to 
the  honor  of  your  commands.  The  length  and  difficulty  of  the  ordi- 
nary means  in  use  have  made  me  think  on  some  help  more  prompt  and 
easy  to  relieve  me  in  the  great  calculations  with  which  I  have  been 
occupied  for  several  years  in  certain  affairs  which  depend  on  the 
occupations  with  which  it  has  pleased  you  to  honor  my  father  for  the 
service  of  his  Majesty  in  Normandy.  I  employed  for  this  investi- 
gation all  the  knowledge  which  my  inclination  and  the  labor  of  my  first 
studies  in  mathematics  have  gained  for  me,  and  after  profound  re- 
flection, I  recognized  that  this  aid  was  not  impossible  to  find. 

MECHANICS  AND  OPTICS  :  HUYGENS.  —  Most  notable  among 
the  successors  of  Galileo  in  mechanics  before  we  reach  Newton 
was  Huygens  of  Holland  (1629-1695)  who  combined  mathematical 
power  with  exceptional  practical  ingenuity.  He  first  (in  1655) 
explained  as  a  ring  the  excrescences  of  Saturn  which  had  been 
misunderstood  by  Galileo  and  others,  publishing  his  discovery  in 
the  occult  form  a7c5dle5g1h1i7l4m2n9o4p2qlr2s1t5u5.  (Annulo  cingitur 
tenuij  piano,  nusquam  cohcerente  ad  eclipticam  inclinato.)  He  also 
discovered  Saturn's  largest  moon.  About  the  same  time  he  made 
his  great  invention  of  the  pendulum  clock.  Accepting  a  call  to 
Paris  by  Colbert  at  the  founding  of  the  French  Academy,  he 
remained  there  from  1666  to  1681. 

In  optics  he  developed  and  maintained  even  in  opposition  to 
the  authority  of  Newton  the  undulatory  or  wave  theory  which 
only  found  general  acceptance  a  century  later.  The  velocity  of 
light  Galileo  had  failed  to  measure  by  means  of  signal  lanterns, 
and  Descartes  had  likewise  been  unable  to  ascertain  it  by  compar- 
ing the  observed  and  computed  instants  of  a  lunar  eclip§e. 
Huygens  points  out  that  even  this  latter  test  does  not  prove  in- 
stantaneous transmission.  Homer's  conclusive  report  on  observa- 
tions of  a  satellite  of  Jupiter  dates  from  1675.  On  this  basis 
Huygens  estimated  the  velocity  of  light  at  600,000  times  that  of 
sound,  —  a  result  about  one-third  too  small. 

The  medium  in  which  light  waves  travel  Huygens  named  the 
ether,  attributing  to  its  particles  three  properties  in  comparison 


HUYGENS   FROM    (EUVRES    COMPLETES,    1899 


BEGINNINGS  OF  MODERN  MATHEMATICAL  SCIENCE    287 

with  air :  extreme  minuteness,  extreme  hardness,  extreme  elas- 
ticity. On  this  basis  he  worked  out  a  consistent  theory  for  re- 
flection and  refraction.  His  discussion  of  the  newly  discovered 
phenomenon  of  double  refraction  in  Iceland  spar  has  been  char- 
acterized as  an  "unsurpassed  example  of  the  combination  of  ex- 
perimental investigation  and  acute  analysis."  The  attendant 
phenomenon  of  polarisation  did  not  escape  him,  but  his  theory 
of  wave  motion  was  not  sufficiently  developed  to  enable  him  to 
explain  the  matter  adequately. 

In  1673  Huygens  published  his  great  work  on  the  pendulum 
(Horologiwn  oscillatorium  sive  de  motu  pendulorum) ,  displaying 
wonderful  skill  in  his  geometrical  treatment  of  the  mechanical 
problems  involved.  The  use  of  wheel  mechanisms  with  weights 
for  measuring  time  had  been  more  or  less  familiar  for  several  cen- 
turies, but  no  effective  means  for  regulating  this  motion  had 
been  devised.  Galileo,  for  example,  observing  the  regularity  of 
pendulum  vibrations,  had  depended  on  repeated  impulses  by 
hand  to  maintain  the  motion.  Huygens  first  made  the  fortunate 
combination  of  the  two  elements,  without  however  inventing  the 
modern  escapement.  He  studied  the  cycloidal  pendulum  for 
which  the  time  of  an  oscillation  would  be  independent  of  the 
amplitude  and  made  precise  determinations  of  the  length  of  the 
seconds-pendulum  at  Paris  and  the  corresponding  value  of  the  im- 
portant constant  g.  The  most  remarkable  achievement  in  his 
treatise  on  the  pendulum  is  the  correct  analysis  of  the  compound 
pendulum  based  on  the  definition :  — 

The  centre  of  oscillation  of  any  figure  whatever  is  that  point  in  the 
line  of  gravity,  whose  distance  from  the  point  of  suspension  is  the 
same  as  the  length  of  the  simple  pendulum  having  the  same  time  of 
vibration  as  the  figure. 

In  the  course  of  the  discussion  he  formulates  the  important  law, 
afterwards  somewhat  generalized  by  others : 

Whenever  any  heavy  bodies  are  set  in  motion  under  the  action  of 
their  own  weight,  their  common  centre  of  gravity  cannot  rise  higher 
than  it  was  at  the  beginning  of  the  motion. 


288  A  SHORT  HISTORY  OF  SCIENCE 

In  computing  the  position  of  the  centre  of  oscillation  he  arrives 

^r>  2 

at  a  fraction  of  the  form  ~  —  >  where  m  denotes  the  mass  of  a 


particle,  r  its  distance  from  the  point  of  suspension.  The  nu- 
merator is  the  so-called  "moment  of  inertia,"  the  denominator  the 
"statical  moment"  of  later  mechanics.  He  shows  that  the  point 
of  suspension  and  the  centre  of  oscillation  are  interchangeable. 

Finally  he  discusses  the  theory  of  centrifugal  force,  proving 
that  it  varies  as  the  square  of  the  velocity  and  inversely  as  the 
radius.  This  subject  he  also  treated  more  fully  in  a  special  mono- 
graph, published  after  his  death  when  Newton  had  already  given 
a  more  general  theory.  His  theorems  are  :  — 

1.  When  equal  bodies  move  with  the  same  velocity  in  unequal 
circles,  the  centrifugal  forces  are  to  each  other  inversely  as  the  diameters, 
so  that  in  the  smaller  circle  the  said  force  is  greater. 

2.  When  equal  movable  bodies  travel  in  the  same  or  equal  circles 
with  unequal  velocities,  the  centrifugal  forces  are  to  each  other  as  the 
squares  of  the  velocities. 

By  experiments  on  a  revolving  sphere  of  clay  which  as  he  antici- 
pated assumed  a  spheroidal  form,  he  explains  the  observed  polar 
flattening  of  Jupiter.  He  infers  that  the  earth  must  also  be 
flattened,  and  makes  a  numerical  estimate  in  anticipation  of  future 
verification.  He  explains  the  effect  on  a  clock  pendulum  of  trans- 
porting it  from  Paris  to  an  equatorial  locality,  where  its  weight  is 
opposed  by  an  increased  centrifugal  force. 

Like  Wallis  (p.  290)  and  Sir  Christopher  Wren  he  accepted  the 
invitation  of  the  Royal  Society  to  attack  the  general  problem  of 
impact.  This  led  ultimately  to  the  publication  eight  years  after 
his  death  of  his  On  the  Motion  of  Bodies  under  Percussion. 
The  theorems  enunciated  deal  with  various  cases  of  central  im- 
pact, one  of  the  most  notable  being  :  — 

By  mutual  impact  of  two  bodies  the  sum  of  the  products  of  the 
masses  into  the  squares  of  their  velocities  is  the  same  before  and  after 
impact. 


FIGI. 


FIG.II. 


FIG.IV: 


// 
/f 


Cenfr. 

Ccrtr. 


HUYGENS'  CLOCK 
(Horologium  Oscillatorium,  1673) 


BEGINNINGS  OF  MODERN  MATHEMATICAL  SCIENCE    289 

—  the  first  formulation  (1669)  of  the  most  comprehensive  law  of 
mechanics,  the  conservation  of  vis  viva. 

Huygens  visited  England  in  1689,  but  made  no  use  of  Newton's 
new  calculus  in  his  published  work.  In  his  History  of  the  Mathe- 
matical Theories  of^  Attraction  and  the  Figure  of  the  Earth, 
Todhunter  says  of  Huygens:  — 

To  him  we  owe  the  important  condition  of  fluid  equilibrium,  that  the 
resultant  force  at  any  point  of  the  free  surface  must  be  normal  to  the 
surface  at  that  point ;  and  this  has  indirectly  promoted  the  knowledge 
of  our  subject.  But  Huygens  never  accepted  the  great  principle  of 
the  mutual  attraction  of  particles  of  matter ;  and  thus  he  contributed 
explicitly  only  the  solution  of  a  theoretical  problem,  namely  the  inves- 
tigation of  the  form  of  the  surface  of  rotating  fluid  under  the  action  of 
a  force  always  directed  to  a  fixed  point. 

WALLIS  AND  BARROW.  —  Before  attempting  to  discuss  the 
extraordinary  work  of  Sir  Isaac  Newton  in  the  whole  field  of 
mathematical  science  a  few  words  should  be  added  concerning  two 
slightly  older  English  mathematicians,  John  Wallis  (1616-1703), 
Savilian  professor  at  Oxford,  and  Isaac  Barrow  (1630-1677), 
Lucasian  professor  at  Cambridge. 

Wallis  in  his  Arithmetic  of  The  Infinites  (1656)  developed 
Cavalieri's  summation  ideas  effectively,  employing  the  new 
Cartesian  geometry  and  a  process  equivalent  to  integration  for 
simple  algebraic  cases.  In  particular,  he  explains  negative  and 
fractional  exponents  in  the  modern  sense,  and  then  proceeds  to 
find  the  area  bounded  by  OX,  the  curve  y  =  axm,  and  any  ordinate 
x  =  h,  —  or  as  we  should  say,  he  integrates  the  function  axm. 
He  develops  ingenious  methods  of  interpolation. 

In  his  Treatise  on  Algebra  he  says :  — 

It  is  to  me  a  theory  unquestionable,  That  the  Ancients  had  some- 
what of  like  nature  with  our  Algebra ;  from  whence  many  of  their  pro- 
lix and  intricate  Demonstrations  were  derived.  .  .  .  But  this  their 
Art  of  Invention,  they  seem  very  studiously  to  have  concealed :  content- 
ing themselves  to  demonstrate  by  Apagogical  Demonstrations,  (or  re- 
ducing to  Absurdity,  if  denied,)  without  showing  us  the  method,  by 


290  A  SHORT  HISTORY  OF  SCIENCE 

which  they  first  found  out  those  Propositions,  which  they  thus  demon- 
strate by  other  ways.  .  .  .  Nonius  '  O  how  well  it  had  been  if  those 
Authors,  who  have  written  in  Mathematics,  had  delivered  to  us  their 
Inventions,  in  the  same  way,  and  with  the  same  Discourse,  as  they 
were  found  out  !  And  not  as  Aristotle  says  of  Artificers  in  Mechanics 
who  show  us  the  Engines  they  have  made,  but  conceal  the  Artifice, 
to  make  them  the  more  admired  !  ' 

His  Analytical  Conic  Sections  (1665)  made  Descartes's  geometri- 
cal ideas  much  more  intelligible,  and  his  Algebra  (1686)  marks  an 
important  step  forward  in  its  systematic  use  of  formulas.  He 
also  wrote  A  Summary  Account  ...  of  the  General  Laws  of  Mo- 
tion, enunciating  the  formulas  for  velocity  after  impact  of  masses 
mi  and  ra2  with  velocities  vi  and  v%  :  — 


mi  +  ra2 

Barrow,  after  varied  adventures,  became  first  Lucasian  professor 
at  the  University  of  Cambridge,  but  resigned  his  chair  six  years 
later  to  his  pupil  Newton.  His  work  on  optics  and  geometry 
contains  a  notable  discussion  of  the  tangent  problem  and  of  what 
he  calls  the  differential  triangle,  so  important  in  modern  elementary 
differential  calculus.  His  general  point  of  view  is  illustrated  by 
the  following  passage  :  — 

Now  as  to  what  pertains  to  these  Surd  numbers  (which,  as  it 
were  by  way  of  reproach  and  calumny,  having  no  merit  of  their  own 
are  also  styled  Irrational,  Irregular,  and  Inexplicable)  they  are  by  many 
denied  to  be  numbers  properly  speaking,  and  are  wont  to  be  banished 
from  arithmetic  to  another  Science  (which  yet  is  no  science),  viz. 
algebra. 

ISAAC  NEWTON,  —  was  born  within  a  year  after  Galileo's  death, 
a  century  after  that  of  Copernicus  —  December  25,  1642  (O.S.). 
Destined  at  first  to  become  a  farmer,  he  was  fortunately  sent  at 
17  to  the  university,  where  he  quickly  and  eagerly  mastered  the 
mathematical  work  of  Euclid,  Descartes  and  Wallis,  and  Kepler's 
Dioptrics.  His  discovery  of  the  general  binomial  theorem  dates 
from  this  time,  and  he  even  ventured  to  attack  the  great  problem 


BEGINNINGS  OF  MODERN  MATHEMATICAL  SCIENCE    291 

of  gravitation  by  carefully  comparing  the  motion  of  the  moon 
with  that  of  a  falling  body  near  the  earth  —  for  which  however 
his  data  were  not  yet  sufficiently  accurate. 

Newton  took  his  B.  A.  degree  in  the  Lent  Term,  1665.  In 
that  spring  the  plague  appeared,  and  for  a  couple  of  years  he  lived 
mostly  at  home,  though  with  occasional  residence  at  Cambridge. 
Probably  at  this  time  his  creative  powers  were  at  their  highest.  His 
use  of  fluxions  may  be  traced  back  to  May,  1665 ;  his  theory  of  gravi- 
tation originated  in  1666;  and  the  foundation  of  his  optical  discov- 
eries would  seem  to  be  only  a  little  later.  In  an  unpublished  mem- 
orandum made  some  years  later  (cancelled,  but  believed  to  be  correct 
in  the  part  here  quoted),  he  thus  described  his  work  of  this  time : 
'  In  the  beginning  of  the  year  1665  I  found  the  method  of  approximat- 
ing Series  and  the  Rule  for  reducing  any  dignity  of  any  Binomial 
into  such  a  series.  The  same  year,  in  May,  I  found  the  method  of 
tangents  of  Gregory  and  Slusius,  and  in  November  had  the  direct 
method  of  Fluxions,  and  the  next  year  in  January  had  the  Theory  of 
Colours,  and  in  May  following  I  had  entrance  into  the  inverse  method 
of  Fluxions.  And  the  same  year  I  began  to  think  of  gravity  extend- 
ing to  the  orb  of  the  Moon,  and  .  .  .  from  Kepler's  Rule  of  the  period- 
ical times  of  the  Planets  being  in  a  sesquialterate  proportion  of  their 
distances  from  the  centers  of  their  orbs  I  deduced  that  the  forces  which 
keep  the  Planets  in  their  orbs  must  (be)  reciprocally  as  the  squares 
of  their  distances  from  the  centers  about  which  they  revolve:  and 
thereby  compared  the  force  requisite  to  keep  the  Moon  in  her  orb 
with  the  force  of  gravity  at  the  surface  of  the  earth,  and  found  them 
answer  pretty  nearly.  All  this  was  in  the  two  plague  years  of  1665 
and  1666,  for  in  those  days  I  was  in  the  prime  of  my  age  for  invention, 
and  minded  Mathematicks  and  Philosophy  more  than  at  any  time 
since/  —  Ball,  Mathematical  Gazette,  July,  1914. 

OPTICS.  —  Interesting  himself  in  the  telescope,  Newton  suc- 
ceeded in  eliminating  the  disturbing  chromatic  aberration  due  to 
unequal  refraction  of  the  different  colors  by  constructing  a  reflect- 
ing telescope  with  a  concave  mirror  in  place  of  a  convex  lens.  On 
the  other  hand,  turning  his  attention  to  the  colors  of  the  solar 
spectrum,  he  wrote  his  Opticks  or  a  Treatise  of  the  Reflections, 
Refractions,  Inflections  and  Colours  of  Light,  published  in  1704. 


292  A  SHORT  HISTORY  OF  SCIENCE 

Disclaiming  any  intention  of  setting  up  speculative  hypotheses,  he 
discusses  the  observed  phenomena  of  refracted  light,  speaking  of 
his  discovery  of  the  different  refrangibility  of  the  rays  of  light  as 
"  in  my  judgment  the  oddest  if  not  the  most  considerable  detection 
which  hath  hitherto  been  made  in  the  operations  of  nature." 
While  he  does  not  insist  upon  it,  he  seems  always  to  have  the 
underlying  idea  that  light  itself  consists  of  minute  particles  —  the 
degree  of  fineness  corresponding  with  the  color — a  theory  which 
held  the  field — thanks  to  his  potent  authority  with  his  too  sub- 
servient followers — against  the  better  undulatory  theory  of  Huy- 
gens  until  the  nineteenth  century.  In  the  experiments  on  which 
this  work  is  based  Newton  not  only  decomposes  light  by  a  refract- 
ing prism  or  series  of  prisms,  but  also  succeeds  in  recombining  the 
component  colors  to  reproduce  the  original  white. 

The  colors  of  objects,  he  says,  are  nothing  more  than  their  power 
to  reflect  one  or  another  kind  of  ray.  And  in  the  rays  again  is 
nothing  other  than  the  power  to  transmit  this  motion  into  our  organ 
of  sense,  in  which  last  finally  arises  the  sensation  of  these  motions  in 
the  form  of  colors. 

He  solves  at  last  the  problem  of  the  rainbow.  All  this  constitutes 
an  immense  advance  over  the  current  Aristotelian  notions. 

THE  THEORY  OF  GRAVITATION:  Principia  —  In  1682  Newton 
returned  to  his  attempt  of  16  years  earlier  to  explain  the  moon's 
motion  by  means  of  the  assumed  influence  of  gravitation.  During 
this  long  interval  French  geographers,  testing  the  supposedly  spher- 
ical shape  of  the  earth,  had  made  a  new  and  more  precise  triangu- 
lation  —  with  the  first  use  of  telescopic  instruments.  Newton's 
earlier  data  had  led  to  a  determination  of  the  acceleration  due 
to  gravity  at  the  distance  of  the  moon  as  13 J  feet  per  minute. 
The  new  data  changed  this  result  to  15,  in  agreement  with  his 
hypothesis  that  the  force  varied  inversely  as  the  square  of  the 
distance.  Stirred  to  the  inmost  depths  of  his  usually  calm  nature 
by  his  realization  that  he  was  approaching  a  solution  of  the  great 
problem,  he  had  to  beg  a  friend  to  complete  his  calculations.  The 
new  astronomy  founded  by  Copernicus,  built  up  byTycho  Brahe, 


NEWTON'S  TELESCOPE  (Great  Astronomers,  R.  S.  Ball). 


A  B 

-.  »=r 

NEWTON'S  THEORY  OF  THE  RAINBOW  (Opticks,  1704). 


BEGINNINGS  OF  MODERN  MATHEMATICAL  SCIENCE    293 

Kepler,  and  Galileo,  was  now  to  be  completely  formulated  and 
mathematically  interpreted  by  Newton's  crowning  discovery  of  a 
single  mechanical  principle  governing  the  whole. 

It  was  now  a  question  of  verifying  the  correctness  of  this  prin- 
ciple by  applying  it  to  all  measured  or  measurable  astronomical 
phenomena.  The  investigation  was  gradually  extended  to  the 
planets,  the  moons  of  Jupiter,  the  tides,  and  even  the  comets. 
Everywhere  the  law  was  verified  that  attraction  varies  as  the  prod- 
uct of  the  masses  and  inversely  as  the  square  of  the  distance. 

The  whole  theory  was  elaborated  in  Newton's  monumental 
Principia  Philosophies  Naturalis  Mathematica  published  in  1687. 
He  begins  this  treatise  with  a  series  of  definitions  and  laws : 

1.  The  quantity  of  matter  is  the  measure  of  the  same,  arising  from 
its  density  and  bulk  conjunctly. 

2.  The  quantity  of  motion  is  the  measure  of  the  same,  arising  from 
the  velocity  and  quantity  of  matter  conjunctly. 

3.  The  innate  force  of  matter  is  a  power  of  resisting,  by  which 
every  body,  as  much  as  in  it  lies,  endeavours  to  persevere  in  its  present 
state,  whether  it  be  of  rest,  or  of  moving  uniformly  forward  in  a 
right  line. 

4.  An  impressed  force  is  an  action  exerted  upon  a  body,  in  order 
to  change  its  state,  either  of  rest,  or  of  moving  uniformly  forward  in 
a  right  line. 

5.  A  centripetal  force  is  that  by  which  bodies  are  drawn  or  im- 
pelled, or  any  way  tend,  towards  a  point  as  to  a  centre. 

These  and  succeeding  definitions  are  followed  by  the  famous 
Laws  of  Motion : 

I.  Every  body  perseveres  in  its  state  of  rest,  or  of  uniform  motion 
in  a  right  line,  unless  it  is  compelled  to  change  that  state  by  forces 
impressed  thereon. 

II.  The  alteration  of  motion  is  ever  proportional  to  the  motive 
force  impressed,  and  is  made  in  the  direction  of  the  right  line  in 
which  that  force  is  impressed. 

III.  To  every  action  there  is  always  opposed  an  equal  reaction : 
or  the  mutual  actions  of  two  bodies  upon  each  other  are  always  equal, 
and  directed  to  contrary  parts.     Corollary  I  continues :  A  body  by  two 


294  A  SHORT  HISTORY  OF  SCIENCE 

forces  conjoined  will  describe  the  diagonal  of  a  parallelogram,  in  the 
same  time  that  it  would  describe  the  sides,  by  those  forces  apart. 

Of  these  laws,  Pearson  in  his  Grammar  of  Science  remarks : 

The  Newtonian  laws  of  motion  form  the  starting-point  of  most 
modern  treatises  on  dynamics,  and  it  seems  to  me  that  physical  sci- 
ence, thus  started,  resembles  the  mighty  genius  of  an  Arabian  tale 
emerging  amid  metaphysical  exhalations  from  the  bottle  in  which  for 
long  centuries  it  has  been  corked  down. 

Passing  to  variable  forces  he  discusses  in  particular  the  motion 
of  a  body  acted  on  by  a  central  attractive  force  —  i.e.  a  force  at- 
tracting it  towards  a  fixed  point.  He  derives  the  law  by  which 
equal  areas  are  described  in  equal  times,  and  shows  that  con- 
versely, if  equal  areas  are  so  described  in  a  plane,  the  determining 
force  must  be  a  central  one.  Turning  to  the  consideration  of  or- 
bits, he  deals  with  the  hypothesis  of  an  elliptical  orbit  with  the 
attracting  force  at  one  of  the  foci,  and  shows  that  the  attractive 
force  must  vary  inversely  as  the  square  of  the  distance  from  that 
focus.  The  same  result  is  obtained  for  the  other  conic  sections. 
These  theorems  applying  to  particles,  he  next  shows  that  the  action 
of  a  homogeneous  sphere  on  an  external  particle  is  the  same  as  if 
its  mass  were  concentrated  at  its  centre,  so  that  the  action  of  two 
such  spheres  on  each  other  is  subject  to  the  laws  already  derived. 

Comparing  planetary  motions  with  those  of  projectiles  which 
had  been  treated  by  Galileo,  Newton  says :  — 

That  the  planets  can  be  held  in  their  paths  is  evident  from  the 
motions  of  projectiles.  A  stone  thrown  is  deflected  from  the  straight 
line  by  its  weight  and  falls  describing  a  curved  line  to  the  earth.  If 
thrown  with  greater  velocity  it  goes  farther,  and  it  could  happen  that 
it  described  a  curve  of  10,100,1000  miles,  and  at  last  went  outside  the 
boundaries  of  the  earth,  and  never  fell  back.  .  .  . 

The  force  of  gravity  for  small  distances  being  sensibly  constant 
in  direction,  causes  motion  in  a  path  approximately  parabolic. 
For  greater  and  greater  ranges  the  change  of  direction  of  the 
force  must  be  taken  account  of  and  the  path  recognized  as  ellipti- 
cal or  hyperbolic.  The  laws  as  stated  deal  with  the  relations  of 


BEGINNINGS  OF  MODERN  MATHEMATICAL  SCIENCE    295 

only  two  mutually  attracting  bodies.  Newton  of  course  appreci- 
ates that  such  a  case  is  purely  ideal  and  that,  since  every  body 
attracts  every  other,  the  result  of  dealing  with  only  two  is  merely 
a  first  approximation  to  the  reality. 

All  planets  he  says  are  mutually  heavy,  therefore,  for  example ;  Jupiter 
and  Saturn  will  attract  each  other  in  the  vicinity  of  their  conjunction 
and  perceptibly  disturb  each  other's  motion.  Similarly  the  Sun  will  dis- 
turb the  motion  of  the  Moon,  and  Sun  and  Moon  will  disturb  our  ocean. 

Newton  prefaced  these  applications  of  the  theory  with  four  rules 
which  should  guide  scientific  men  in  making  hypotheses.  These  in 
their  final  shape,  are  to  the  following  effect :  (1)  We  should  not  assume 
more  causes  than  are  sufficient  and  necessary  for  the  explanation  of 
observed  facts.  (2)  Hence,  as  far  as  possible,  similar  effects  must  be 
assigned  to  the  same  cause ;  for  instance,  the  fall  of  stones  in  Europe 
and  America.  (3)  Properties  common  to  all  bodies  within  reach  of 
our  experiments  are  to  be  assumed  as  pertaining  to  all  bodies;  for 
instance,  extension.  (4)  Propositions  in  science  obtained  by  wide  in- 
duction are  to  be  regarded  as  exactly  or  approximately  true,  until 
phenomena  or  experiments  show  that  they  may  be  corrected  or  are 
liable  to  exceptions.  The  substance  of  these  rules  is  now  accepted 
as  the  basis  of  scientific  investigation.  Then*  formal  enunciation  here 
serves  as  a  landmark  in  the  history  of  thought.  —  Mathematical 
Gazette,  July,  1914. 

Every  new  satellite,  says  Brewster  in  his  Life  of  Newton,  every 
new  asteroid,  every  new  comet,  every  new  planet,  every  new  star 
circulating  round  its  fellow,  proclaims  the  universality  of  Newton's 
philosophy,  and  adds  fresh  lustre  to  his  name.  It  is  otherwise  however 
in  the  general  history  of  science.  The  reputation  achieved  by  a  great 
invention  is  often  transferred  to  another  which  supersedes  it,  and  a 
discovery  which  is  the  glory  of  one  age  is  eclipsed  by  the  extension  of 
it  in  another.  ...  It  is  the  peculiar  glory  of  Newton,  however, 
that  every  discovery  in  the  heavens  attests  the  universality  of  his 
laws,  and  adds  a  greener  leaf  to  the  laurel  chaplet  which  he  wears. 

Shrinking  always  from  publicity 1  and  controversy,  Newton  like 
Copernicus  had  gradually  perfected  his  great  work,  but,  like  Co- 

1  In  one  instance  he  authorized  publication  of  one  of  his  works  "so  it  be  without 
my  name  to  it :  for  I  see  not  what  there  is  desirable  in  public  esteem,  were  I  able 


296  A  SHORT  HISTORY  OF  SCIENCE 

pernicus,  Newton  might  never  have  published  it  but  for  the  for- 
tunate urgency  of  a  faithful  disciple,  Edmund  Halley. 

NEWTON'S  MATHEMATICS  :  FLUXIONS.  —  Newton's  services  to 
mathematics  itself  were  not  less  original  and  momentous  than 
to  celestial  mechanics. 

His  extraordinary  abilities  .  .  .  enabled  him  within  a  few  years  to  per- 
fect the  more  elementary  .  .  .  processes,  and  to  distinctly  advance 
every  branch  of  mathematical  science  then  studied,  as  well  as  to  create 
several  new  subjects.  There  is  hardly  a  branch  of  modern  mathe- 
matics which  cannot  be  traced  back  to  him  and  of  which  he  did  not 
revolutionize  the  treatment. 

In  pure  geometry  Newton  did  not  establish  any  new  methods, 
but  no  modern  writer  has  ever  shown  the  same  power  in  using  those 
of  classical  geometry,  and  he  solved  many  problems  in  it  which  had 
previously  baffled  all  attempts.  In  algebra  and  the  theory  of  equa- 
tions he  introduced  the  system  of  literal  indices,  established  the  bi- 
nomial theorem  .  .  .,  and  created  no  inconsiderable  part  of  the  theory 
of  equations.  ...  He  always  by  choice,  avoided  using  trigonometry 
in  his  analysis,  ...  In  analytical  geometry  he  introduced  the 
modern  classification  of  curves  into  algebraical  and  transcendental; 
and  established  many  of  the  fundamental  properties  of  asymptotes, 
multiple  points  and  isolated  loops.  He  illustrated  these  by  an  ex- 
haustive discussion  of  cubic  curves.  —  Ball. 

Newton's  greatest  mathematical  achievement  was  of  course  the 
invention  of  the  fluxional  or  infinitesimal  calculus.  In  his  Treatise 
of  the  Method  of  Fluxions  and  Infinite  Series  he  says :  — 

1.  Having  observed  that  most  of  our  modern  Geometricians 
neglecting  the  synthetical  Method  of  the  Ancients,  have  applied 
themselves  chiefly  to  the  analytical  Art,  and  by  the  Help  of  it  have 
overcome  so  many  and  so  great  Difficulties,  that  all  the  Speculations 
of  Geometry  seem  to  be  exhausted,  except  the  Quadrature  of  Curves, 
and  some  other  things  of  a  like  Nature  which  are  not  yet  brought  to 
Perfection :  To  this  End  I  thought  it  not  amiss,  for  the  sake  of  young 

to  acquire  and  maintain  it :  it  would  perhaps  increase  my  acquaintance,  the  thing 
which  I  study  chiefly  to  decline."  Again  in  1675  he  writes  "I  was  so  persecuted 
with  discussions  arising  out  of  my  theory  of  light,  that  I  blamed  my  own  impru- 
dence for  parting  with  so  substantial  a  blessing  as  my  quiet,  to  run  after  a  shadow." 


BEGINNINGS  OF  MODERN  MATHEMATICAL  SCIENCE    297 

Students  in  this  Science,  to  draw  up  the  following  Treatise ;  wherein 
I  have  endeavored  to  enlarge  the  Boundaries  of  Analyticks,  and  to 
make  some  Improvements  in  the  Doctrine  of  Curved  Lines. 

—  surely  a  sufficiently  modest  introduction  of  perhaps  the  most 
important  step  in  the  progress  of  mathematical  science. 

Something  further  as  to  the  evolution  of  his  theory  of  Fluxions 
may  be  indicated,  without  too  much  technical  detail,  by  the  fol- 
lowing passages  from  Brewster :  — 

Having  met  with  an  example  of  the  method  of  Fermat,  in  Schoo- 
ten's  Commentary  on  the  Second  Book  of  Descartes,  Newton  suc- 
ceeded in  applying  it  to  affected  equations,  and  determining  the  pro- 
portion of  the  increments  of  indeterminate  quantities.  These  incre- 
ments he  called  moments,  and  to  the  velocities  with  which  the  quan- 
tities increase  he  gave  the  names  of  motions,  velocities  of  increase,  and 
fluxions.  He  considered  quantities  not  as  composed  of  indivisibles, 
but  as  generated  by  motion ;  and  as  the  ancients  considered  rectangles 
as  generated  by  drawing  one  side  into  the  other,  that  is,  by  moving 
one  side  upon  the  other  to  describe  the  area  of  the  rectangle,  so  Newton 
regarded  the  areas  of  curves  as  generated  by  drawing  the  ordinate  into 
the  abscissa,  and  all  indeterminate  quantities  as  generated  by  con- 
tinual increase.  Hence,  from  the  flowing  of  time  and  the  moments 
thereof,  he  gave  the  name  of  flowing  quantities  to  all  quantities  which 
increase  in  time,  that  of  fluxions  to  the  velocities  of  their  increase,  and 
that  of  moments  to  their  parts  generated  in  moments  of  time. 

Newton  then  proceeds  to  show  the  application  of  the  propositions 
to  the  solution  of  the  twelve  following  problems,  many  of  which  were 
at  that  time  entirely  new : 

1.  To  draw  tangents  to  curve  lines. 

2.  To  find  the  quantity  of  the  crookedness  of  lines. 

3.  To  find  the  points  distinguishing  between  the  concave  and 
convex  portions  of  curved  lines. 

4.  To  find  the  point  at  which  lines  are  most  or  least  curved. 

5.  To  find  the  nature  of  the  curve  line  whose  area  is  expressed 
by  any  given  equation. 

6.  The  nature  of  any  curve  line  being  given,  to  find  other  lines 
whose  areas  may  be  compared  to  the  area  of  that  given  line. 

7.  The  nature  of  any  curve  line  being  given,  to  find  its  area  when 


298  A  SHORT  HISTORY  OF  SCIENCE 

it  may  be  done ;   or  two  curved  lines  being  given,  to  find  the  relation 
of  their  areas  when  it  may  be. 

8.  To  find  such  curved  lines  whose  lengths  may  be  found,  and  also 
to  find  their  lengths. 

9.  Any  curve  line  being  given,  to  find  other  lines  whose  lengths 
may  be  compared  to  its  length,  or  to  its  area,  and  to  compare  them. 

10.  To  find  curve  lines  whose  areas  shall  be  equal  or  have  any 
given  relations  to  the  length  of  any  given  curve  line  drawn  into  a  given 
right  line. 

11.  To  find  the  length  of  any  curve  line  when  it  may  be. 

12.  To  find  the  nature  of  a  curve  line  whose  length  is  expressed  by 
any  given  equation  when  it  may  be  done. 

Such  were  the  improvements  in  the  higher  geometry  which  Newton 
had  made  before  the  end  of  1666. 

Such  is  a  brief  account  of  the  mathematical  writings  of  Sir  Isaac 
Newton,  not  one  of  which  was  voluntarily  communicated  to  the  world 
by  himself.  The  publication  of  his  Universal  Arithmetic  is  said  to 
have  been  made  by  Whiston  against  his  will ;  and,  however  this  may 
be,  it  was  an  unfinished  work,  never  designed  for  the  public.  The 
publication  of  his  Quadrature  of  Curves,  and  of  his  Enumeration  of 
Curve  Lines,  was  in  Newton's  opinion  rendered  necessary,  in  con- 
sequence of  plagiarisms  from  the  manuscripts  of  them  which  he 
had  lent  to  his  friends,  and  the  rest  of  his  analytical  writings  did 
not  appear  till  after  his  death. 

An  account  of  Newton's  very  important  work  in  analytic  geome- 
try and  the  theory  of  algebraic  equations  lies  outside  the  range  of 
the  present  work. 

Much  of  Newton's  reluctance  to  publish  his  more  revolutionary 
theories  may  be  attributed  to  his  distaste  for  controversy,  and  he 
was  unfortunately  involved  not  only  in  such  issues  as  to  priority 
as  his  own  reticence  invited,  but  also  in  defending  himself  against 
attacks  on  philosophic  grounds.  The  character  of  some  of  these 
may  be  illustrated  by  the  following  passages  from  an  eminent 
critic,  Bishop  Berkeley :  — 

He  who  can  digest  a  second  or  third  fluxion,  a  second  or  third 
difference,  need  not,  methinks,  be  squeamish  about  any  point  in  Di- 
vinity. 


BEGINNINGS  OF  MODERN  MATHEMATICAL  SCIENCE    299 

And  what  are  these  fluxions?  The  velocities  of  evanescent  in- 
crements. And  what  are  these  same  evanescent  increments?  They 
are  neither  finite  quantities,  nor  quantities  infinitely  small,  nor  yet 
nothing.  May  we  not  call  them  ghosts  of  departed  quantities  ? 

In  regard  to  the  controversy  between  the  friends  of  Newton 
and  those  of  Leibnitz  as  to  priority  in  the  invention  of  the  calculus, 
Newton  himself  says  in  a  celebrated  scholium :  — 

The  correspondence  which  took  place  about  ten  years  ago,  be- 
tween that  very  skilful  geometer  G.  G.  Leibnitz  and  myself,  when  I 
had  announced  to  him  that  I  possessed  a  method  of  determining 
maxima  and  minima,  of  drawing  tangents,  and  of  performing  similar 
operations,  which  was  equally  applicable  to  surds  and  to  rational 
quantities,  and  concealed  the  same  in  transposed  letters,  involving 
this  sentence,  (Data  Aequatione  quotcunque  Fluentes  quantitates  in- 
volvente,  Fluxiones  invenire,  et  vice  versa),  this  illustrious  man  re- 
plied that  he  also  had  fallen  on  a  method  of  the  same  kind,  and 
he  communicated  his  method,  which  scarcely  differed  from  my  own, 
except  in  the  forms  of  words  and  notation  (and  in  the  idea  of  the 
generation  of  quantities). 

Of  the  controversy  as  a  whole  Newton's  biographer  Brewster 
remarks : 

The  greatest  mathematicians  of  the  age  took  the  field,  and  states- 
men and  princes  contributed  an  auxiliary  force  to  the  settlement  of 
questions  upon  which,  after  the  lapse  of  nearly  200  years,  a  verdict 
has  not  yet  been  pronounced. 

Although  the  honour  of  having  invented  the  calculus  of  fluxions, 
or  the  differential  calculus,  has  been  conferred  upon  Newton  and 
Leibnitz,  yet,  as  in  every  other  great  invention,  they  were  but  the 
individuals  who  combined  the  scattered  lights  of  their  predecessors, 
and  gave  a  method,  a  notation,  and  a  name  to  the  doctrine  of  quanti- 
ties infinitely  small. 

In  studying  this  controversy,  after  the  lapse  of  nearly  a  century 
and  a  half,  when  personal  feelings  have  been  extinguished,  and  national 
jealousies  allayed,  it  is  not  difficult,  we  think,  to  form  a  correct  esti- 
mate of  the  claims  of  the  two  rival  analysts,  and  of  the  spirit  and 
temper  with  which  they  were  maintained.  The  following  are  the 
results  at  which  we  have  arrived : 


300  A  SHORT  HISTORY  OF  SCIENCE 

1st  —  That  Newton  was  the  first  inventor  of  the  Method  of  Flux- 
ions ;  that  the  method  was  incomplete  in  its  notation ;  and  that  the 
fundamental  principle  of  it  was  not  published  to  the  world  till  1687, 
twenty  years  after  he  had  invented  it. 

2d  —  That  Leibnitz  communicated  to  Newton  in  1677  his  Differential 
Calculus,  with  a  complete  system  of  notation,  and  that  he  published 
it  in  1684,  three  years  before  the  publication  of  Newton's  Method. 

—  Brewster. 

It  is  said  that  when  the  Queen  of  Prussia  asked  Leibnitz  his  opinion 
of  Sir  Isaac  Newton,  he  replied  that  taking  mathematicians  from  the 
beginning  of  the  world  to  the  time  when  Sir  Isaac  lived,  what  he  had 
done  was  much  the  better  half ;  and  added  that  he  had  consulted  all 
the  learned  in  Europe  upon  some  difficult  points  without  having 
any  satisfaction  and  that  when  he  applied  to  Sir  Isaac,  he  wrote 
him  in  answer  by  the  first  post,  to  do  so  and  so,  and  then  he  would 
find  it. 

The  exalted  estimation  in  which  Newton's  genius  has  been 
held  in  later  times  may  be  illustrated  by  the  following  passages. 

The  great  Newtonian  Induction  of  Universal  Gravitation  is  in- 
disputably and  incomparably  the  greatest  scientific  discovery  ever 
made,  whether  we  look  at  the  advance  which  it  involved,  the  extent 
of  the  truth  disclosed,  or  the  fundamental  and  satisfactory  nature  of 
this  truth.  —  Whewell 

The  efforts  of  the  great  philosopher  .  .  .  were  always  super- 
human ;  the  questions  which  he  did  not  solve  were  incapable  of  solu- 
tion in  his  time.  —  Arago. 

Newton  was  the  greatest  genius  that  ever  existed,  and  the  most 
fortunate,  for  we  cannot  find  more  than  once  a  system  of  the  world 
to  establish.  —  Lagrange. 

His  own  attitude  is  sufficiently  indicated  in  his  statements :  — 

I  do  not  know  what  I  may  appear  to  the  world,  but,  to  myself, 
I  seem  to  have  been  only  like  a  boy  playing  on  the  seashore,  and  divert- 
ing myself  in  now  and  then  finding  a  smoother  pebble  or  a  prettier 
shell  than  ordinary,  whilst  the  great  ocean  of  truth  lay  all  undis- 
covered before  me. 

If  I  have  seen  farther  than  Descartes,  it  is  by  standing  on  the 
shoulders  of  giants.  (See  also  Appendix.) 


BEGINNINGS  OF  MODERN  MATHEMATICAL  SCIENCE    301 

LEIBNITZ.  —  Newton's  great  contemporary  and  scientific  rival 
Leibnitz  has  been  called  the  Aristotle  of  the  seventeenth  century. 
Born  in  1646  at  Leipsic,  he  took  his  doctor's  degree  at  20  and  was 
immediately  offered  a  university  professorship.  Alchemy,  diplo- 
macy, philosophy,  mathematics,  all  shared  his  energetic  attention. 
In  the  last  he  invented  a  calculating  machine  and  the  differential 
calculus.  In  regard  to  the  machine  Klein  says:  — 

merely  the  formal  rules  of  computation  are  essential,  for  only  these 
can  be  followed  by  the  machine.  It  cannot  possibly  have  an  intuitive 
conception  of  the  meaning  of  the  numbers.  It  is  thus  no  accident  that 
a  man  so  great  as  Leibnitz  was  both  father  of  purely  formal  mathe- 
matics and  inventor  of  the  first  calculating  machine. 

He  became  librarian  at  Hannover,  founded  the  Academy  of 
Sciences  in  Berlin,  and  was  instrumental  in  the  organization  of 
similar  bodies  in  St.  Petersburg,  Dresden,  and  Vienna.  His  ad- 
vanced ideas  on  education  may  be  inferred  from  his  remark  — 

We  force  our  youths  first  to  undertake  the  Herculean  labor  of 
mastering  different  languages,  whereby  the  keenness  of  the  intellect 
is  often  dulled,  and  condemn  to  ignorance  all  who  lack  knowledge  of 
Latin. 

But  for  the  overshadowing  genius  of  Newton,  Leibnitz'  service 
to  the  progress  of  science  would  have  been  even  greater  than  it 
actually  was.  Comparing  their  work  in  mathematics  where  their 
competition  was  keenest,  it  should  be  appreciated  that  while  New- 
ton's work  in  mathematical  science  was  incomparably  greater  in 
range,  it  was  Leibnitz  who  gave  to  the  differential  calculus  the 
better  form  and  notation  out  of  which  our  own  has  grown. 

It  appears  that  Fermat,  the  true  inventor  of  the  differential  cal- 
culus, considered  that  calculus  as  derived  from  the  calculus  of  finite 
differences  by  neglecting  infinitesimals  of  higher  orders  as  compared 
with  those  of  a  lower  order  .  .  .  Newton,  through  his  method  of 
fluxions,  has  since  rendered  the  calculus  more  analytical,  he  also  sim- 
plified and  generalized  the  method  by  the  invention  of  his  binomial 
theorem.  Leibnitz  has  enriched  the  differential  calculus  by  a  very 
happy  notation.  —  Laplace. 


302  A  SHORT  HISTORY  OF  SCIENCE 

Leibnitz'  sense  of  mathematical  form  was  also  well  exemplified 
by  his  important  algebraic  invention  of  determinants.  In  regard 
to  numbers  he  says :  — 

The  imaginary  numbers  are  a  fine  and  wonderful  refuge  over 
the  divine  spirit,  almost  an  amphibium  between  being  and  not  being. 

Leibnitz's  discoveries  lay  in  the  direction  in  which  all  modern  pro- 
gress in  science  lies,  in  establishing  order,  symmetry,  and  harmony, 
i.e.  comprehensiveness  and  perspicuity,  —  rather  than  in  dealing 
with  single  problems,  in  the  solution  of  which  followers  soon  at- 
tained greater  dexterity  than  himself.  —  Merz. 

Leibnitz  believed  he  saw  the  image  of  creation  in  his  binary  arith- 
metic, in  which  he  employed  only  two  characters,  unity  and  zero. 
Since  God  may  be  represented  by  unity,  and  nothing  by  zero,  he 
imagined  that  the  Supreme  Being  might  have  drawn  all  things  from 
nothing,  just  as  in  the  binary  arithmetic  all  numbers  are  expressed 
by  unity  with  zero.  This  idea  was  so  pleasing  to  Leibnitz,  that  he 
communicated  it  to  the  Jesuit  Grimaldi,  President  of  the  Mathematical 
Board  of  China,  with  the  hope  that  this  emblem  of  the  creation  might 
convert  to  Christianity  the  reigning  emperor  who  was  particularly 
attached  to  the  sciences.  —  Laplace. 

HALLEY  :  PREDICTION  OF  COMETS.  —  In  applying  Newton's 
theories  to  known  comets  his  friend  and  disciple  Halley  made  the 
astonishing  discovery  that  some  of  them  instead  of  visiting  the 
solar  system  once  for  all,  actually  described  elliptical  orbits  of 
vast  extent  and  great  eccentricity  about  the  sun.  Among  these 
he  found  one  which  having  appeared  in  1531,  1607,  and  1682, 
should,  if  his  identifications  were  correct,  return  in  1759.  This 
bold  prediction  was  fulfilled,  and  Halley's  comet  has  not  only 
reappeared  in  1835  and  1910,  but  has  even  been  traced  back  almost 
to  the  beginning  of  our  era.  A  second  similar  prediction  of  Halley 
awaits  verification  in  the  year  2255. 

In  physics,  Halley  enunciated  for  spherical  lenses  and  mirrors 

the  correct  formula  -  =  —  -f  —    and  that  for  the  barometric 
/      «i      «2 

determination   of   altitudes.     His   mathematical   work   included 
graphical  discussion  of  the  cubic  and  biquadratic  equations,  a 


BEGINNINGS  OF  MODERN  MATHEMATICAL  SCIENCE    303 

method  of  computing  logarithms,  and  an  edition  of  Apollonius 
from  both  Greek  and  Arabic  sources.  In  his  paper  on  An  Esti- 
mate of  the  Degrees  of  the  Mortality  of  Mankind,  drawn  from  cu- 
rious Tables  of  the  Births  and  Funerals  at  the  City  of  Breslau; 
with  an  Attempt  to  ascertain  the  Price  of  Annuities  upon  Lives, 
he  laid  the  foundations  of  a  new  and  important  branch  of  applied 
mathematics.  Having  in  boyhood  occupied  himself  with  mag- 
netic experiments,  in  middle  life  he  travelled  in  the  tropics  and 
made  the  first  magnetic  map,  published  in  1701  under  the  title  "A 
general  chart,  showing  at  one  view  the  variation  of  the  com- 
pass." Drawing  curves  on  this  chart  through  points  of  declina- 
tion, he  invented  a  graphical  method  of  wide  future  usefulness. 
From  naval  captain  he  became  professor  of  geometry  at  Oxford, 
then  astronomer  royal  till  his  death  in  1742.  One  of  his  most 
notable  achievements  in  astronomy  was  the  discovery  of  actual 
changes  in  the  apparent  relative  positions  of  the  fixed  stars, 
Aldebaran,  Arcturus,  and  Sirius  —  answering  a  question  centuries 
old. 

REFERENCES  FOR  READING 

Ball.     Short  History  of  Mathematics.     Chapters  XV,  XVI. 
Berry.     History  of  Astronomy.     Chapters  VIII,  IX,  X. 
Brewster.     Memoir  of  Sir  Isaac  Newton. 
Lodge.     Pioneers  of  Science.     VII,  VIII,  IX. 
Mach.     Science  of  Mechanics. 
Newton.     Principia. 


CHAPTER  XIV 

NATURAL  AND  PHYSICAL  SCIENCE  IN  THE  EIGHTEENTH 

CENTURY 

The  seventeenth  and  eighteenth  centuries  mark  the  period  in 
which,  owing  to  the  use  of  the  several  vernacular  languages  of  Europe 
in  the  place  of  the  medieval  Latin,  thought  became  nationalized. 
Thus  it  was  that  .  .  .  people  could  make  journeys  of  exploration  in 
the  region  of  thought  from  one  country  to  another,  bringing  home 
with  them  new  and  fresh,  ideas.  Such  journeys  .  .  .  were  those  of 
Voltaire  to  England  in  1726  ...  of  Adam  Smith  in  1765  to  France. 

—  M  erz. 

IN  the  preface  to  one  of  his  volumes  of  essays,  Lord  Morley 
speaks  of  the  eighteenth  century  as  the  scientific  Renaissance. 
Such  it  undoubtedly  was,  for  it  was  in  this  century  and  es- 
pecially in  its  latter  half,  that  chemistry,  geology,  botany,  zoology* 
and  physics,  began  to  make  deep  impression  on  the  learned  world, 
while  astronomy  and  mathematics  ventured  upon  bolder  and 
more  far-reaching  generalizations  than  they  had  ever  before  made. 
Science  as  a  special  discipline,  or  as  a  branch  of  learning  worthy 
of  the  highest  consideration,  had  as  yet  scarcely  begun  to  make 
itself  felt,  but  the  names  of  Newton  and  Descartes  were  frequently 
heard  in  the  salons  of  Paris  and  keen  observers  like  Voltaire  per- 
ceived the  rising  of  a  new  tide  in  the  affairs  of  men.  A  growth  of 
popular  interest  might  naturally  have  been  expected  after  the 
great  discoveries  of  the  sixteenth  and  seventeenth  centuries.  What 
was  not  looked  for  was  the  concurrence  of  those  political  and 
social  upheavals  ever  since  rightly  known  as  revolutions ;  viz.  the 
French  Revolution,  the  American  Revolution  and,  probably  most 
important  of  all,  the  Industrial  Revolution. 

CHEMISTRY  :  DECLINE  OF  THE  PHLOGISTON  THEORY.  —  We 
have  already  touched  upon  the  work  of  Boerhaave  and  Hales 
in  the  field  of  organic  chemistry,  so-called,  and  may  now  pass  on 

304 


NATURAL  AND  PHYSICAL  SCIENCE,  1700-1800       305 

to  the  studies  of  Black,  Bergmann  and  others  on  the  gas  sylvestre 
(carbonic  acid)  of  Van  Helmont.  Dr.  Joseph  Black  of  Edinburgh, 
a  physician  of  note  and,  as  we  shall  see,  one  of  the  first  to  put 
the  science  of  heat  on  a  sure  foundation,  seeking  to  explain  the 
phenomena  accompanying  the  making  and  the  slaking  of  "quick0 
lime,  —  phenomena  now  familar  to  every  beginner  in  chemistry 
but  in  1750  puzzling  to  all,  —  remembered  that  Hales  had  found 
that  "air"  could  be  driven  off  from  certain  substances  by  heat- 
ing, and  suspected  that  in  the  burning  of  limestone  to  make 
quicklime,  something  might  be  driven  off,  the  loss  of  which 
would  make  it  lighter.  This  something  he  tried  to  obtain  by 
causing  acid  to  act  upon  limestone  (in  the  ordinary  laboratory 
fashion  of  to-day)  and  collecting  the  gas  evolved  by  the  aid  of 
Hales'  pneumatic  trough.  He  next  weighed  the  gas  and  the 
remaining  limestone  and  found  that  the  weight  of  the  former 
agreed  with  the  loss  of  weight  of  the  latter.  He  then  reversed  the 
experiment,  causing  "fixed  air"  (as  he  called  it)  to  bubble  through 
a  solution  of  lime,  whereupon,  as  he  had  anticipated,  a  white, 
chalk-like  powder  appeared  and  fell  to  the  bottom.  This  simple 
experiment  proved  extremely  fruitful,  and  we  can  now  see  that  in 
its  use  of  analysis  and  synthesis,  in  its  partly  quantitative  char- 
acter, and  in  the  chemical  reasoning  employed,  it  was  also  highly 
instructive.  Best  of  all,  it  did  not  require  any  hypothetical, 
immaterial  or  mystical  "phlogiston"  for  satisfactory  explanation 
of  all  the  hitherto  puzzling  phenomena  involved.  Black  invented 
for  the  gas  thus  driven  off  by  heat  or  acid  the  term  "fixed  air,"  be- 
cause it  was  evidently  "fixed"  in  the  limestone  or  chalky  precipi- 
tate, and  because  any  gas  or  vapor  not  obviously  something  else, 
was  still  supposed  to  be  "  air,"  —  the  true  nature  and  chemical  com- 
position of  the  atmosphere  being  still  (in  1750)  quite  unknown. 

At  this  point  Bergmann,  a  Swedish  chemist  of  distinction,  by 
the  use  of  litmus  (which  Boyle  had  recommended  as  a  test  for  acids) 
and  other  means,  discovered  that  the  "fixed  air"  of  Black  is  an 
acid,  and  accordingly  named  it  "aerial  acid."  Bergmann  also 
weighed  the  new  gas,  finding  it  heavier  than  air,  and  discovered 
that  it  is  very  soluble  in  water, 
x 


306  A  SHORT  HISTORY  OF  SCIENCE 

To  sum  up :  It  was  now  known  that  there  exists  an  invisible, 
odorless  gas,  resembling  air  but  heavier  than  air  and  more  soluble 
in  water ;  that  it  is  acid,  and  capable  of  attaching  itself  to  lime, 
making  a  kind  of  chalk ;  that  it  will  not  support  life,  yet  is  present 
in  the  human  breath,  as  well  as  in  some  mineral  waters ;  and  that 
it  is  given  off  during  fermentations.  It  only  remained  for  Lavoisier 
to  discover  (in  1779)  that  this  gas  is  compounded  of  two  very 
common  elements  —  carbon  and  oxygen  —  tightly  bound  together, 
and  may  therefore  be  called,  as  it  often  is  today,  "  carbonic  acid." 
But  before  this  could  happen  other  investigations  had  to  prepare 
the  way,  and  especially  the  discovery  of  the  new  "element," 
oxygen. 

A  NEW  CHEMISTRY.  PRIESTLEY  AND  LAVOISIER.  —  We  have 
now  reached  a  period  of  remarkable  activity  and  rapid  progress 
in  chemical  research.  While  Black  was  hard  at  work  upon  chemi- 
cal problems  in  Scotland,  and  Bergmann  in  Sweden,  Cavendish 
was  similarly  engaged  in  England,  and  in  1766  reported  to  the 
Royal  Society  his  discovery  of  a  new  kind  of  gas  to  which,  for 
the  reason  that  it  took  fire  whenever  flame  was  applied  to  it, 
and  also  because  he  believed  it  to  be  the  cause  of  the  occasional 
explosions  in  mines,  he  gave  the  name  "inflammable  air." 
Cavendish  obtained  this  gas  by  treating  iron,  tin,  zinc,  or  other 
metals  with  sulphuric  acid,  very  much  as  Black  had  obtained 
fixed  air  by  treating  limestone  with  acids.  Inflammable  air 
was,  however,  obviously  quite  unlike  fixed  air,  since  it  was 
lighter  than  air  —  not  heavier  —  and  was  readily  burned.  It 
resembled  it,  nevertheless,  in  that  a  lighted  candle  plunged  into 
it  went  out,  and  animals  died  in  it  just  as  they  did  in  fixed 
air.  It  had  another  peculiar  property ;  viz.  that  of  forming  with 
air  an  explosive  mixture.  This  new  gas  as  we  now  know  was 
hydrogen. 

Not  long  after,  in  1772,  other  new  gases  were  separated 
and  studied;  viz.  nitrogen  by  Rutherford,  and  nitric  oxide  by 
Priestley.  It  was  on  August  1,  1774,  however,  that  Priestley 
made  his  most  important  discovery,  and  one  that  proved  to  be  the 
very  corner-stone  of  the  splendid  edifice  in  which  modern  chem- 


NATURAL  AND  PHYSICAL  SCIENCE,  1700-1800      307 

istry  now  dwells,  namely,  the  discovery  of  oxygen.  Joseph  Priestley, 
fearless  reformer,  Unitarian  clergyman,  and  tireless  experimenter  in 
natural  philosophy,  had  already  made  important  and  interesting 
discoveries  when,  in  1774,  as  stated  above,  he  decomposed  by 
heat  the  reddish  powder  obtained  by  calcining  mercury,  and 
collected  and  examined  the  gas  given  off.  Candles  and  glowing 
coals  burned  in  this  gas  with  extraordinary  energy,  and  mice  lived 
in  it  under  a  bell  glass  even  longer  than  in  ordinary  air.  And, 
since  it  was  derived  from  a  burnt,  i.e.  dephlogisticated,  metal 
and  yet  was  colorless  and  odorless  like  ordinary  air,  Priestley 
named  it  "dephlogisticated  air."  The  following  is  his  own 
account  of  his  work :  — 

There  are,  I  believe,  very  few  maxims  in  philosophy  that  have 
laid  firmer  hold  upon  the  mind  than  that  air,  meaning  atmospheric 
air,  is  a  simple  elementary  substance,  indestructible  and  unalterable 
at  least  as  much  so  as  water  is  supposed  to  be.  In  the  course  of  my 
inquiries  I  was,  however,  soon  satisfied  that  atmospheric  air  is  not  an 
unalterable  thing;  for  that,  according  to  my  first  hypothesis,  the 
phlogiston  with  which  it  becomes  loaded  from  bodies  burning  in  it, 
and  the  animals  breathing  it,  and  various  other  chemical  processes, 
so  far  alters  and  depraves  it  as  to  render  it  altogether  unfit  for  inflam- 
mation, respiration,  and  other  purposes  to  which  it  is  subservient; 
and  I  had  discovered  that  agitation  in  the  water,  the  process  of  vege- 
tation, and  probably  other  natural  processes,  restore  it  to  its  original 
purity.  .  .  . 

Having  procured  a  lens  of  twelve  inches  diameter  and  twenty 
inches  focal  distance,  I  proceeded  with  the  greatest  alacrity,  by  the 
help  of  it,  to  discover  what  kind  of  air  a  great  variety  of  substances 
would  yield,  putting  them  into  the  vessel,  which  I  filled  with  quick- 
silver, and  kept  inverted  in  a  basin  of  the  same.  .  .  .  With*  this  ap- 
paratus, after  a  variety  of  experiments  ...  on  the  1st  of  August, 
1774,  I  endeavored  to  extract  air  from  mercurius  calcinatits  per  se; 
and  I  presently  found  that,  by  means  of  this  lens,  air  was  expelled  from 
it  very  readily.  Having  got  about  three  or  four  times  as  much  as 
the  bulk  of  my  materials,  I  admitted  water  to  it,  and  found  that  it 
was  not  imbibed  by  it.  But  what  surprised  me  more  than  I  can 
express  was  that  a  candle  burned  in  this  air  with  a  remarkably  vigorous 


308  A  SHORT  HISTORY  OF  SCIENCE 

flame,  very  much  like  that  enlarged  flame  with  which  a  candle  burns 
in  nitrous  oxide,  exposed  to  iron  or  liver  of  sulphur ;  but  as  I  had  got 
nothing  like  this  remarkable  appearance  from  any  kind  of  air  besides 
this  particular  modification  of  vitreous  air,  and  I  knew  no  vitreous  acid 
was  used  in  the  preparation  of  mercurius  calcinatus,  I  was  utterly  at 
a  loss  to  account  for  it.  ... 

The  flame  of  the  candle,  besides  being  larger,  burned  with  more 
splendor  and  heat  than  in  that  species  of  nitrous  air;  and  a  piece 
of  red-hot  wood  sparkled  in  it,  exactly  like  paper  dipped  in  a  solution 
of  nitre,  and  it  consumed  very  fast ;  an  experiment  that  I  had  never 
thought  of  trying  with  dephlogisticated  nitrous  air. 

...  I  had  so  little  suspicion  of  the  air  from  the  mercurius  cal- 
cinatus, etc.,  being  wholesome,  that  I  had  not  even  thought  of  apply- 
ing it  to  the  test  of  nitrous  air;  but  thinking  (as  my  reader  must 
imagine  I  frequently  must  have  done)  on  the  candle  burning  in  it 
after  long  agitation  in  water,  it  occurred  to  me  at  last  to  make  the 
experiment ;  and,  putting  one  measure  of  nitrous  air  to  two  measures 
of  this  air,  I  found  not  only  that  it  was  diminished,  but  that  it  was 
diminished  quite  as  much  as  common  air,  and  that  the  redness  of  the 
mixture  was  likewise  equal  to  a  similar  mixture  of  nitrous  and  com- 
mon air.  .  .  .  The  next  day  I  was  more  surprised  than  ever  I  had 
been  before  with  finding  that,  after  the  above-mentioned  mixture  of 
nitrous  air  and  the  air  from  mercurius  calcinatus  had  stood  all  night, 
...  a  candle  burned  in  it,  even  better  than  in  common  air. 

At  almost  the  same  time  (1775)  Scheele,  a  Swedish  chemist, 
independently  discovered  the  same  gas.  "Scheele  remained  a 
poor  apothecary  all  his  life,  yet  was  really  one  of  the  first  chemists 
of  Europe."  His  name  for  oxygen  was  "empyreal  air." 

But  if  Black  and  Cavendish  and  Priestley  and  Scheele  and 
others  laid  the  foundations  of  modern  chemistry,  it  was  the  yet 
more  famous  Lavoisier,  who,  building  upon  the  results  of  his 
predecessors,  began  the  erection  of  the  present  lofty  superstruc- 
ture. Lavoisier  soon  dismissed  forever  the  long-standing,  mysti- 
cal theory  of  phlogiston  through  his  unremitting  use  of  the  balance, 
for  the  introduction  and  use  of  which  in  analysis  he  has  been 
rightly  called  "  the  founder  of  quantitative  chemistry."  By 
means  of  the  balance  he  proved  that  when  metals  are  burnt  in 


NATURAL  AND  PHYSICAL  SCIENCE,  1700-1800       309 

air,  the  resulting  substances  weigh  more  than  did  the  metal ;  and 
that  if  burnt  in  a  closed  space  the  loss  in  weight  of  the  air  equals  the 
gain  in  weight  of  the  metal.  And  when,  finally,  he  reversed  the 
experiment,  decomposing  the  red  powder  of  burnt  mercury  as 
Priestley  had  done,  and  weighing  as  before,  he  found  that  the  loss 
of  weight  of  the  red  powder  at  the  end  was  exactly  equal  to  the 
weight  of  the  " dephlogisticated  air"  driven  off. 

Lavoisier  named  the  gas  thus  derived  oxygen  (acid  producer), 
because  its  compounds  seemed  to  him  to  be  chiefly  acids.  And 
since  Black's  "fixed  air"  was  Bergmann's  "aerial  acid,"  and  could 
be  made  by  burning  charcoal  in  air,  Lavoisier  suspected  that 
fixed  air  contained  oxygen  as  well  as  carbon.  Accordingly,  he 
proceeded  to  burn  charcoal  in  pure  oxygen,  and  obtained  fixed 
air  or  aerial  acid,  which  he  thereupon  analyzed,  proving  that 
100  parts  contained  72  of  oxygen  and  28  of  carbon.  He  there- 
fore named  it  carbonic  acid.  Afterward,  by  burning  a  diamond 
in  pure  oxygen  and  obtaining  carbonic  acid,  he  proved  that  one  of 
the  precious  "stones"  is  really  a  form  of  carbon.  Priestley  died 
clinging  to  the  phlogiston  theory,  but  his  dephlogisticated  air 
had  now  become  Lavoisier's  oxygen.  Lavoisier,  one  of  the  most 
brilliant  men  of  science  in  any  age,  continued  as  long  as  he  lived 
to  do  remarkable  work.  He  repeated  with  more  precision  the 
experiment  of  Cavendish  on  the  synthesis  of  water  from  inflam- 
mable air  and  ordinary  air  (or  oxygen),  and  named  the  former 
hydrogen  (water  producer).  But,  unfortunately  for  science, 
Lavoisier,  since  he  had  held  government  office  as  a  farmer-gen- 
eral, found  no  favor  in  the  eyes  of  the  leaders  of  the  French 
Revolution  and  on  May  18,  1794,  at  the  age  of  51,  he  was  guil- 
lotined. Thus  was  the  end  of  the  eighteenth  century,  otherwise 
in  most  respects  favorable  to  science  and  other  learning,  dis- 
graced by  a  foul  blot  on  civilization,  as  had  been  the  end  of  the 
sixteenth  by  the  burning  of  Giordano  Bruno ;  the  latter  a  victim  to 
misdirected  religious  conservatism,  Lavoisier  to  equally  misdirected 
political  radicalism. 

THE  SYNTHESIS  OF  WATER.  —  In  1784  Cavendish  added  to  his 
other  brilliant  discoveries  that  of  the  composition  of  water.     He 


310  A  SHORT  HISTORY  OF  SCIENCE 

had  himself  discovered  inflammable  air  or  hydrogen,  and  now 
he  found  that  by  exploding  a  mixture  of  this  gas  with  oxygen, 
water  was  produced. 

By  experiments  with  the  globe  it  appeared,  says  Cavendish, 
that  when  inflammable  and  common  air  are  exploded  in  a  proper 
proportion,  almost  all  the  inflammable  air,  and  near  one-fifth  the  com- 
mon air,  lose  their  elasticity  and  are  condensed  into  dew.  And  by 
this  experiment  it  appears  that  this  dew  is  plain  water,  and  conse- 
quently that  almost  all  the  inflammable  air  is  turned  into  pure  water. 

In  order  to  examine  the  nature  of  the  matter  condensed  on  firing 
a  mixture  of  dephlogisticated  and  inflammable  air,  I  took  a  glass  globe, 
holding  8800  grain  measures,  furnished  with  a  brass  cock  and  an  ap- 
paratus for  firing  by  electricity.  This  globe  was  well  exhausted  by  an 
air-pump,  and  then  filled  with  a  mixture  of  inflammable  and  dephlo- 
gisticated air  by  shutting  the  cock,  fastening  the  bent  glass  tube 
into  its  mouth,  and  letting  up  the  end  of  it  into  a  glass  jar  inverted 
into  water  and  containing  a  mixture  of  19,500  grain  measures  of 
dephlogisticated  air,  and  37,000  of  inflammable  air;  so  that,  upon 
opening  the  cock,  some  of  this  mixed  air  rushed  through  the  bent  tube 
and  filled  the  globe.  The  cock  was  then  shut  and  the  included  air 
fired  by  electricity,  by  means  of  which  almost  all  of  it  lost  its  elasticity 
(was  condensed  into  water  vapors).  The  cock  was  then  again  opened 
so  as  to  let  in  more  of  the  same  air  to  supply  the  place  of  that  de- 
stroyed by  the  explosion,  which  was  again  fired,  and  the  operation 
continued  till  almost  the  whole  of  the  mixture  was  let  into  the  globe 
and  exploded.  By  this  means,  though  the  globe  held  not  more  than  a 
sixth  part  of  the  mixture,  almost  the  whole  of  it  was  exploded  therein 
without  any  fresh  exhaustion  of  the  globe. 

BEGINNINGS  OF  MODERN  IDEAS  OF  SOUND.  —  We  have  seen 
above  that  the  Greeks  were  deeply  interested  in  sound,  as  well 
as  in  music.  The  invention  of  the  monochord  with  the  dis- 
covery by  Pythagoras  of  the  relation  between  the  length  of  a 
vibrating  string  and  the  'sound  which  it  produces  was  the  first 
step  in  the  right  direction,  although  any  mystical  relation  between 
sound  and  number  such  as  the  Pythagoreans  inferred  has  no  basis. 

From  Pythagoras  to  Galileo  little  or  no  progress  was  made. 
Galileo  recognized  that  sound  is  due  to  vibrations  in  the  air  falling 


NATURAL  AND  PHYSICAL  SCIENCE,   1700-1800       311 

upon  the  ear-drum,  and  in  one  of  his  dialogues  explains  concord 
and  dissonance  by  concurrence  or  conflict  of  such  vibrations. 
He  shows  how  vibrations  causing  sound  may  be  made  visible,  and 
how  to  measure  the  relative  length  of  sound  waves  by  scraping 
a  brass  plate  with  a  chisel,  thereby  making  dust  on  the  plate  take 
up  positions  in  parallel  lines.  That  air  is  really  the  intermediary 
was  proved  in  1705  by  Hawksbee's  experiment  of  placing  a  clock 
in  a  vacuum. 

After  Galileo,  the  studies,  mathematical  and  experimental,  of 
Newton,  Euler,  and  Sauveur  (1653-1715)  brought  acoustics  to 
the  point  where  it  was  taken  up  and  given  much  of  its  present 
form  by  Chladni  (1756-1827)  —  "the  Father  of  Modern  Acous- 
tics." Sauveur,  eminent  physicist  and  musician,  deserves  more 
than  passing  notice  from  the  fact  that  he  "had  neither  voice  nor 
ear"  (being  half  deaf  and  dumb)  and  yet  achieved  distinction  for 
his  original  researches  in  both  sound  and  music.  Intended  by  his 
parents  for  the  church,  he  early  manifested  delight  in  mechanical 
contrivances  and  in  arithmetic,  but  the  course  of  his  life  was 
determined  by  a  copy  of  Euclid  which  accidentally  came  to  his 
notice.  He  thereupon  abandoned  an  ecclesiastical  career  and, 
having  in  consequence  lost  the  support  of  his  relatives,  obtained  a 
livelihood  by  teaching  mathematics,  becoming  a  professor  of 
that  subject  in  1686.  During  the  remainder  of  his  life  the  study 
of  acoustics,  and  particularly  the  scientific  theory  of  music  (in 
which  he  was  the  first  to  draw  attention  to  overtones  or  har- 
monics) occupied  much  of  his  attention.  Many  of  his  papers 
were  published  in  the  Memoirs  of  the  French  Academy,  1700-1714. 
The  work  of  Chladni  at  the  beginning  of  the  nineteenth  century 
laid  broad  and  deep  the  foundations  of  acoustics  as  we  know  that 
science  to-day,  and  upon  this  foundation  Helmholtz  and  Tyndall 
in  the  middle  of  that  century  reared  a  large  part  of  the  modern 
superstructure.  Chladni  carried  much  further  the  experiments  of 
Galileo  on  vibrating  plates,  substituting  a  violin  bow  for  the 
chisel,  and  sand  for  dust  on  the  plates,  obtaining  thereby  that 
wonderful  variety  of  figures  which  is  nowadays  demonstrated 
to  beginners  by  every  teacher  of  natural  philosophy.  He  also 


312  A  SHORT  HISTORY  OF  SCIENCE 

devised  a  simple  method  of  counting  the  number  of  vibrations 
corresponding  with  each  note. 

THE  BEGINNINGS  OF  MODERN  IDEAS  OF  HEAT:  LATENT  AND 
SPECIFIC  HEAT  ;  CALORIMETRY.  —  The  earlier  ideas  of  the  nature 
of  heat  are  not  unlike  those  of  light.  Theories  of  emission  were 
at  first  preferred  for  both,  and  present  ideas  of  vibration  or 
undulation  have  appeared  only  recently.  Heat  was  even  re- 
garded as  an  imponderable  yet  material  substance,  "  caloric," 
emitted  by  hot  bodies  and  absorbed  by  cold  ones.  High  temper- 
ature meant  the  presence,  and  low  temperature,  the  absence,  of 
caloric.  The  rise  of  mercury  in  the  thermometer  tube  was  ex- 
plained as  due  to  the  expansion  of  the  mercury  not,  as  to-day,  by 
increase  of  distance  between  molecules,  but  by  the  addition  of 
caloric  and  the  consequent  increase  of  total  material.  Francis 
Bacon  remarked  on  the  problem  of  heat  and  in  an  interesting 
passage  on  the  proper  method  of  its  study  shows  that  he  knew 
many  of  its  phenomena,  including  its  development  "in  bodies 
heated  by  rubbing."  But  it  remained  for  Black,  of  Edinburgh, 
whose  work  on  fixed  air  or  carbonic  acid  we  have  dwelt  upon 
above,  to  make  the  fundamental  researches  which  paved  the 
way  both  for  the  study  of  the  theory  of  heat  by  Rumford  at  the 
end  of  the  eighteenth  century,  and  for  its  industrial  uses  by 
Watt  in  steam  engineering  in  the  middle  of  that  century.  Black, 
while  experimenting  on  heating  and  cooling,  discovered  that 
heat  may  be  applied  to  boiling  water,  or  to  water  containing 
melting  ice,  without  raising  the  temperature.  Obviously,  such 
applied  heat  must  either  be  lost  or  somehow  become  latent. 
Further  experiments  showed  that  once  the  ice  is  all  melted,  or 
once  the  escape  of  steam  is  stopped  by  covering  the  water  in  a 
closed  vessel,  the  temperature  begins  to  rise ;  the  heat  is  no  longer 
concealed,  lost,  or  absorbed,  but  produces  obvious  effects.  Ap- 
parently the  lost  heat  was  somehow  used  in  melting  the  ice  and 
in  making  the  steam.  These  and  other  experiments  by  Black 
proved  suggestive  to  Watt,  who  at  this  time  was  trying  to  improve 
upon  the  air-and-steam  engine  of  Newcomen,  in  which  atmos- 
pheric pressure  was  used  to  push  a  piston  in  a  cylinder  filled  with 


NATURAL  AND  PHYSICAL  SCIENCE,  1700-1800      313 

and  then  emptied  of  steam,  and  it  was  largely  by  the  aid  of 
Black's  studies  on  latent  heat  that  Watt  was  enabled  and  en- 
couraged to  persevere  and  push  to  completion  his  own  epoch- 
making  discoveries  in  steam  engineering. 

Black  was  also  the  first  to  recognize  and  investigate  what  we 
know  today  as  "specific"  heat  and,  by  means  of  a  cavity  in  a  block 
of  ice  into  which  various  heated  bodies  were  brought,  to  weigh  the 
water  each  would  produce  while  cooling  from  the  same  tempera- 
ture, —  in  other  words  to  invent  and  use  the  calorimeter. 

EIGHTEENTH  CENTUEY  RESEARCHES  ON  LIGHT.  —  These  start 
from  the  great  work  of  Newton,  and  especially  of  Huygens,  in 
the  previous  century,  and  continue  with  the  fruitful  inventions 
of  the  achromatic  telescope  by  Hall  in  1733,  and  the  work  of 
Dollond,  an  English  optician,  upon  achromatic  lenses,  leading 
up  to  the  construction  in  1758  of  achromatic  telescope  objectives. 
The  achromatic  telescope  now  became  a  serviceable  instrument, 
but  the  compound  microscope  had  to  wait  more  than  half  a  cen- 
tury longer  for  correspondingly  serviceable  achromatic  objectives. 
It  was  not  until  the  opening  of  the  nineteenth  century  that  much 
further  progress  was  made  in  our  knowledge  of  light.  __It  is 
rather  for  progress  in  sound,  in  heat,  and  in  electricity,  that 
eighteenth  century  physical  science  is  chiefly  notable. 

BEGINNINGS  OF  MODERN  IDEAS  OF  ELECTRICITY  AND  MAG- 
NETISM. —  The  seventeenth  century  had  witnessed  no  great 
progress  in  these  subjects,  and  the  sixteenth  century  work  of 
William  Gilbert  stood  as  almost  the  only  important  contribu- 
tion to  our  knowledge  of  them  until  about  1730.  Von  Guericke, 
following  suggestions  of  Gilbert,  had,  it  is  true,  made  a  rude 
electrical  machine  which  he  described  in  a  work  published  in 
1672,  and  had  observed  the  electric  spark,  which  with  his  machine 
was  so  small  as  to  be  seen  only  in  the  dark  and  to  be  heard  with 
difficulty.  Much  more  important  were  the  observations  of  Francis 
Hawksbee  (or  Hauksbee),  "one  of  the  most  active  experimental 
philosophers  of  his  age,"  and  one  of  the  first  to  study  capillary 
action,  who  in  1705  communicated  to  the  Royal  Society  several 
curious  experiments  on  what  he  called  "the  mercurial  phosphorus/' 


314  A  SHORT  HISTORY  OF  SCIENCE 

showing  that  light  could  be  produced  by  passing  common  air 
through  mercury  placed  in  a  well-exhausted  receiver.  These 
phenomena,  which  had  been  observed  before  Hawksbee's  time 
and  had  been  variously  explained,  were  attributed  by  him  to 
electricity,  for  he  remarked  their  resemblance  to  lightning.  Like 
Newton  he  used  a  revolving  glass  globe,  rubbed  by  the  hand,  to 
generate  electricity.  These  and  other  results  he  published  in 
1707-1709. 

Further  investigations  by  Wall,  Gray  and  Wheeler,  Desagu- 
liers,  Dufay,  and  many  others  prepared  the  way  for  Watson, 
Franklin,  Galvani,  and  Volta,  whose  investigations  in  the  latter 
half  of  the  eighteenth  century,  added  to  those  just  referred  to, 
would  alone  make  that  century  forever  famous  in  the  history  of 
science.  On  these  brilliant  discoveries  we  can  only  briefly  touch. 
Wall  (1708)  compared  the  electric  spark  and  its  crackling  to 
lightning  and  thunder.  Gray  and  Wheeler  (1729)  and  later  Dufay 
created  what  has  been  called  an  epoch  in  the  history  of  electricity 
by  discovering  that  different  bodies  differ  in  electrical  conductiv- 
ity, while  Desaguliers  confirmed  and  extended  their  results. 
Dufay  (1699-1739)  repeated  these  and  other  experiments  and 
discovered  that  there  are  two  kinds  of  electricity,  positive  and  nega- 
tive, or,  as  he  called  them  from  their  source  of  origin,  vitreous  and 
resinous.  Watson  undertook  with  the  aid  of  a  party  of  friends 
from  the  Royal  Society  to  determine  the  velocity  of  the  electric 
current  and  found  "that  through  the  whole  length  of  a  wire  12,276 
feet  long,  the  velocity  of  electricity  was  instantaneous."  Many 
others  had  also  made  important,  if  minor,  contributions  to  the  new 
science  of  the  electric  "fluid"  —  for  like  heat  (caloric)  electricity 
was  regarded  as  material  though  imponderable  —  before  that 
science  was  further  developed  and  widely  popularized  by  Frank- 
lin. 

Benjamin  Franklin  (1706-1790)  was  not  the  first  American  to  do 
good  work  for  science,  but  he  was  the  first  to  gain  wide  renown 
in  it  together  with  an  international  reputation.  Even  before 
1750,  Franklin  had  argued  that  all  the  known  phenomena  of  elec- 
tricity had  their  counterpart  in  lightning,  but  it  was  not  until 


NATURAL  AND  PHYSICAL  SCIENCE,    1700-1800      315 

June,  1752,  that  he  made  his  famous  kite  experiment,  which  showed 
that  lightning  is  really  an  electrical  phenomenon,  since  a  Leyden 
jar  can  be  charged  from  the  skies,  and  at  the  same  time  proved  that 
atmospheric  and  machine-made  (frictional)  electricity  are  one  and 
the  same  thing.  This  daring  experiment  was  performed  also  in 
Europe  at  about  the  same  time  by  others,  and  marks  one  of  the 
greatest  triumphs  of  science  in  any  age,  for  it  simplified  and  to  a 
great  extent  explained  one  of  the  oldest  and  most  awe-inspiring 
phenomena  of  nature.  Furthermore,  by  correlating  the  thunder- 
bolts of  Zeus  and  the  shocks  of  a  Leyden  jar  with  the  sparks  of  an 
electrical  machine,  and  even  with  those  from  a  cat's  back,  it  tended 
mightily  to  inspire  confidence  in  natural  philosophy  and  to  lessen 
correspondingly  the  universal  dread  of  unseen,  mysterious,  and 
supposedly  supernatural,  powers  or  influences.  Other  important 
work  in  electricity  was  done  in  this  century  by  Beccaria  in  Italy, 
Canton  and  Symmer  in  England,  and  many  others. 

THE  BEGINNINGS  OF  MODERN  IDEAS  OF  THE  EARTH.  —  The 
eighteenth  century  saw  important  progress  also  in  biological 
subjects,  —  although  the  word  biology  was  not  yet  born,  and 
zoology  and  botany,  even,  were  still  undifferentiated  and  closely 
associated  with  geological  knowledge  under  the  broad  and  hospi- 
table Aristotelian  term  "natural  history."  Physiology  meanwhile 
retained  its  close  connection  with  its  parent  medical  science,  its 
logical  relations  to  zoology  and  botany  being  generally  unrecog- 
nized. Inquiries  were,  however,  on  foot  destined,  as  we  can 
now  see,  to  bring  about  changes,  namely,  to  differentiate  natural 
history  into  geology,  botany,  and  zoology  and,  finally,  to  integrate 
the  two  latter  sciences  into  one  greater  than  either,  viz.  biology. 

It  must  have  occurred  to  the  thoughtful  reader  of  the  foregoing 
pages  that  the  four  elements  of  the  Greeks  and  their  followers 
have  by  this  time  lost  their  primitive  character,  and  become 
highly  complex  compounds  or  combinations  of  phenomena.  Air, 
for  example,  by  the  end  of  the  eighteenth  century  was  proved  to 
be  a  mixture  of  various  elements  and  compounds,  to  possess  weight 
and  to  exert  pressure,  to  have  no  part  in  abhorrence  of  vacua,  and 
to  be  the  seat  of  marvellous  aqueous  and  electrical  phenomena. 


316  A  SHORT  HISTORY  OF  SCIENCE 

Fire,  long  a  mystery,  was  by  this  time  regarded,  not  as  an  "ele- 
ment," but  as  a  luminous  centre  of  intense  chemical  change. 
Water,  above  all,  —  abundant,  important,  susceptible  of  metamor- 
phism  into  ice,  snow,  dew,  fog,  and  steam,  —  had  surrendered  the 
secrets  of  its  very  being,  having  been  split  apart  into  hydrogen  and 
oxygen  gases,  and  created  or  restored  as  a  liquid  by  bringing  these 
two  gases  together  at  high  temperature.  Here  also,  as  in  Frank- 
lin's kite  experiment,  mystery,  if  not  dispelled,  was  at  least  driven 
back ;  and  the  suggestion  became  natural  and  reasonable,  —  If 
only  enough  were  known,  might  not  many  other  mysteries  in  na- 
ture be  lessened,  if  not  altogether  done  away  ? 

But,  while  these  more  comprehensible  and  more  rational  ideas 
of  air,  fire,  and  water  were  now  the  common  property  of  natural 
philosophy,  natural  history  still  held  unsolved  most  of  its  ancient 
problems.  The  earth,  for  example,  while  probably  no  longer  re- 
garded as  one  of  the  four  elements,  was  as  yet  a  standing  puzzle 
in  respect  to  its  origin,  both  as  a  whole  and  as  to  its  parts. 
Astronomy  had  proved  the  planetary  character  of  the  earth 
but  had  not  yet  suggested  for  it  or  for  its  fellows  any  natural, 
as  opposed  to  supernatural,  origin,  and  was  entirely  silent  as  to 
the  sources  and  history  of  the  earth's  crust,  so  rich  in  minerals, 
metals,  volcanoes,  earthquakes,  soils,  craters,  gases  and  par- 
ticularly fossils,  —  those  mute  remains  which  could  no  longer 
be  disposed  of  as  freaks  of  nature,  but  must  be  looked  upon 
as  indefeasible  witnesses  to  a  prehistoric  past.  Leonardo  in 
the  fifteenth  and  Palissy  in  the  sixteenth  century  revived  the 
ideas  of  Pythagoras  and  Xenophanes  as  to  the  true  nature  of  fos- 
sils, but  no  further  progress  of  note  was  made  for  upwards  of  a 
hundred  years,  when  about  1670  Steno,  a  Dane,  and  Scilla,  an 
Italian,  published  studies  on  petrifactions,  illustrated  with  draw- 
ings. Hooke,  already  referred  to  (p.  268),  Ray,  the  naturalist,  and 
later  (1695)  Woodward,  made  collections  of  chalk,  gravel,  coal, 
and  marble,  and  gravely  discussed  their  meaning  in  terms  of  the 
Flood  of  Noah.  In  this  unsatisfactory  position  matters  stood  at 
the  end  of  the  seventeenth  century,  and  it  was  not  until  nearly  the 
middle  of  the  eighteenth,  viz.  in  1740,  that  much  further  progress 


NATURAL  AND  PHYSICAL  SCIENCE,  1700-1800       317 

was  made.  At  that  time  Lazzaro  Moro  put  forward  the  view  that 
the  rocks  must  have  been  in  process  of  formation  when  fossils  were 
included  in  them,  and  that  the  earth's  crust  evidently  consists  of 
strata,  superimposed  one  upon  another.  He  also  reasoned  from 
the  character  of  the  included  fossils,  back  to  the  character  of  the 
rocks  containing  them,  —  arguing  that  some  must  have  been 
laid  down  in  fresh  water,  others  in  salt  water,  and  hence  some  in 
rivers  or  lakes,  and  some  in  the  sea. 

In  1765  the  first  school  of  mines  of  which  we  have  record  was 
established  at  Freiberg,  in  Saxony,  and  here  appeared  in  1775  a 
student  of  the  natural  history  of  minerals  and  of  the  earth,  viz. 
Abraham  Werner,  son  of  an  Inspector  of  Mines  at  Freiberg,  and 
eventually  a  popular  teacher  there  of  mining  and  geology.  Wer- 
ner's name  is  associated  with  a  special  school  —  the  Neptunists 
—  who,  following  him,  held  that  the  crust  of  the  earth  had  been 
laid  down  in  water.  In  opposition,  another  school  —  theVul- 
canists — arose,  holding  that  it  has  come  rather  by  fire,  volcanoes, 
and  the  like. 

Towards  the  end  of  the  eighteenth  century,  Dr.  Hutton  of 
Edinburgh,  and  William  Smith,  an  English  surveyor,  made  patient, 
accurate,  and  detailed  studies  of  fossils  and  their  distribution,  and 
of  erosion  and  other  work  of  water,  over  a  considerable  area,  and 
published,  the  former  a  Theory  of  the  Earth  (1788),  the  latter  a 
geological  map  of  England  (1815).  These  formed  a  solid  basis 
for  that  epoch-making  work  by  Lyell,  in  1830,  to  which  we  shall 
refer  hereafter.  Hutton_deserves  to  be  especially  remembered 
with  honorjor  his  msistencethat  the  bestinterpreter  of  thepast 
js  thej)resent ;  that^we_wouJd_kTinw  finw~rnrks  were  formedlages 
ago,  we  have  only  to  observe  how  they  are  being  formed  today. 
This  simple  doctrine  of  "  unif  ormitarianism "  was  nolTonlyan 
inspiration  to  Lyell,  but,  largely  through  Lyell,  prepared  the  way 
for  Darwinism  and  other  evolutionary  ideas  requiring  time  with 
slow  change,  in  the  scientific  revolution  of  the  nineteenth  century. 

EIGHTEENTH  CENTURY  PROGRESS  IN  BOTANY,  ZOOLOGY,  ETC.  — 
The  great  world  of  plant  and  animal  life,  even  at  the  middle  of 
the  eighteenth  century,  was  still  almost  unexplored  and  unclas- 


318  A  SHORT  HISTORY  OF  SCIENCE 

sified.  The  early  work  of  Aristotle  in  zoology  and  of  Theophras- 
tus  in  botany,  as  well  as  that  of  Gesner  in  the  sixteenth  century 
and  Ray  and  Grew  and  Malpighi  and  Willughby  in  the  seventeenth 
have  been  referred  to  above,  but  until  we  come  to  Buff  on  (1707— 
1785),  the  French  naturalist,  and  Linnaeus  (Carl  von  Linne)  (1707- 
1778),  the  Swedish,  we  meet  with  no  other  great  name,  and  find 
no  important  researches  on  record  within  the  field  of  natural 
history.  Buffon's  special  contribution  to  science  was  a  fine  work 
on  "Natural  History,"  and  an  infectious  enthusiasm  which  so 
popularized  him  that  20,000  people  are  said  to  have  mourned  at 
his  funeral. 

Linngeus  was  also  an  immensely  popular  writer  and  teacher  of 
natural  history,  who  at  the  same  time  advanced  the  science  of 
botany  by  introducing  an  order  and  system  into  the  classifica- 
tion of  plants  which  facilitated  their  comparative  study.  It  is 
not  too  much  to  say  that  Linneeus  established  botany  as  a 
science.  He  also  did  much  work  upon  animals  and  minerals,  but 
his  famous  dictum,  "stones  grow,  plants  grow  and  live,  and 
animals  grow,  live,  and  feel,"  while  emphasizing  an  important 
and  fundamental  similarity  in  natural  objects,  has  long  since  lost 
whatever  standing  it  may  once  have  had.  It  is  not  so  much  in 
their  properties  as  in  their  substance  that  stones,  plants,  and 
animals  agree,  and  the  greatest  service  done  by  Linnaeus  for 
science  was  his  insistence  on  the  importance  of  the  careful  ob- 
servation of  likeness  and  difference,  and  of  clear  and  accurate 
description.  To  this  end  he  introduced  a  binomial  system,  so 
that  closer  and  more  accurate  classification  in  natural  history 
was  facilitated  and  ever  after  employed.  His  first  great  work,  Sys- 
tema  natures,  was  published  in  1735.  His  collection  of  plants, 
insects,  books,  etc.  now  forms  the  nucleus  of  the  Linnsean 
Society  library  in  London,  founded  in  1788.  The  special  pro- 
cedures adopted  by  him  proved  to  be  artificial,  and  were  soon  re- 
placed by  a  more  natural  basis  of  classification  introduced  by  de 
Jussieu ;  but  the  scientific  names  applied  to  many  animals  (includ- 
ing man  himself,  Homo  sapiens)  and  many  plants,  are  still  in  com- 
mon use  throughout  the  scientific  world. 


NATURAL  AND  PHYSICAL  SCIENCE,  1700-1800      319 

In  the  time  of  Aristotle  man  took  his  place  naturally  at  the  head 
of  the  other  animals.  .  .  .  But  the  influence  of  religion  and  phi- 
losophy did  not  long  permit  of  this  association.  Man  came  to  be 
regarded  as  the  chef-d'oeuvre  of  creation,  a  thing  apart  '  a  little  lower 
than  the  angels/  In  the  eighteenth  century  came  a  startling  change, 
man  was  wrenched  from  this  detached  and  isolated  attitude  and 
linked  on  once  more  to  the  beasts  of  the  field.  This  was  the  work 
of  Linnaeus.  .  .  . 

Buffon  did  not  classify,  he  described  .  .  .  the  genius  of  Linnaeus 
lay  in  classification.  Order  and  method  were  with  him  a  passion. 
In  his  Systema  natures  he  fixed  the  place  of  man  in  nature,  arranging 
Homo  sapiens  as  a  distinct  species  in  the  order  Primates,  together 
with  the  apes,  the  lemurs  and  the  bats.  —  Haddon. 

PROGRESS  IN  COMPARATIVE  ANATOMY  AND  PHYSIOLOGY.  — The 
seventeenth  century  was  peculiarly  rich  in  physiological  and 
anatomical  discoveries,  largely  because  it  was  endowed  with  a  man 
of  genius  in  physiology,  Harvey,  and  with  a  new  and  valuable 
instrument,  —  the  compound  microscope.  It  is  true  that  this 
last  did  not  fulfil  its  promise,  because  of  mechanical  defects,  but 
it  was  good  enough  to  enable  Malpighi  to  clinch  with  positive 
proof  Harvey's  theory  of  the  circulation  of  the  blood,  besides  re- 
vealing certain  anatomical  features  of  spleen  and  kidney,  hitherto 
unknown.  In  1743  Haller  (1707-1777)  of  Berne  proved  that  the 
muscles  do  not  depend  for  their  contractility,  as  had  been  sup- 
posed, upon  "vital  spirits"  sent  in  through  the  nerves,  but  possess 
independent  and  intrinsic  powers  of  contraction  even  when  sepa- 
arated  from  the  nervous  system  or  from  the  body  itself.  This  im- 
portant discovery,  together  with  much  excellent  anatomical  work, 
was  made  by  Haller  at  Gottingen,  where  he  was  professor  "of 
anatomy,  surgery,  and  botany"  and  whither  he  soon  drew 
large  numbers  of  enthusiastic  pupils.  Haller  will  long  be  re- 
membered, not  only  for  his  great  work  in  physiology  and  in  teaching, 
but  also  as  one  of  the  founders  of  comparative  anatomy.  In 
this  subject,  however,  he  was  soon  left  far  behind  by  the  famous 
John  Hunter  (1728-1793)  and  William  Hunter,  his  brother. 

We  must  not  omit  to  observe  that  with  comparative  anatomy, 


320  A  SHORT  HISTORY  OF  SCIENCE 

comparative  botany,  and  comparative  geology  and  mineralogy, 
eighteenth  century  science  was  now  laying  solid  foundations  for 
the  great  generalizations  of  the  nineteenth  century.  Compar- 
ative physiology,  even,  was  making  a  beginning,  with  the  ex- 
periments of  Bonnet  (1720-1793)  upon  the  reproduction  of  lost 
parts  in  the  lower  animals,  and  of  Spallanzani  (1729-1799)  upon 
spontaneous  generation.  To  consideration  of  the  labors  of  these 
last  we  shall  return. 

THE  INDUSTRIAL  REVOLUTION.  INVENTIONS.  POWER. — Far- 
reaching  in  their  consequences  as  were  the  French  Revolution  of 
1793  and  the  American  Revolution  of  1776,  it  is  the  Industrial 
Revolution,  especially  after  1770,  with  which  the  student  of  the 
history  of  science  has  chiefly  to  deal.  Before  the  Industrial  Revolu- 
tion, i.e.  almost  everywhere  before  1760  or  even  1770,  whatever 
machinery  existed  was  run  mostly  by  hand  or  foot,  and  was  hence 
easily  operated  in  the  separate  homes  of  the  workers.  But  within 
the  next  thirty  years  the  factory  system  had  come,  with  coopera- 
tive labor  in  or  about  some  central  power-plant,  and  with  ma- 
chinery driven  by  water  power  or  steam.  With  this  change,  which 
increased  the  output  of  the  individual,  and  took  work  and  workers 
out  of  the  home,  a  revolution  began  which  is  still  affecting  every 
country  and  has  modified  the  very  structure  of  human  society. 

The  change  was  probably  imminent  in  any  event,  for  the  use 
of  water  power  had  begun  before  the  introduction  of  steam;  but 
the  perfection  of  the  steam-engine  by  Watt,  who  as  we  have  seen, 
was  powerfully  aided  by  the  scientific  studies  of  his  fellow  country- 
man, Black,  on  heat,  steam,  evaporation,  and  calorimetry,  greatly 
hastened,  and  soon  made  almost  universal,  the  mighty  change. 
Henceforth  machinery  was  to  become  the  handmaid  of  toil,  and 
to  bring  with  it  not  only  factory  industry  in  place  of  home  indus- 
try but,  before  long,  improved  means  of  transportation,  effecting  a 
virtual  shrinkage  of  the  world  and  a  far  closer  contact  of  mankind. 

Almost  coinciding  with  the  introduction  of  water  power  and 
steam  power,  came  a  great  burst  of  invention.  The  spinning 
"jenny"  and  the  "water  frame"  came  almost  hand  in  hand  with 
the  "  mule  "  and  the  "  power  loom ; "  while,  as  if  to  meet  these  on  the 


NATURAL  AND  PHYSICAL  SCIENCE,    1700-1800      321 

cotton  field,  the  cotton  "gin"  (engine),  was  invented  (by  Eli 
Whitney  of  Connecticut)  to  replace  the  slow  and  tedious  process 
of  separating  the  cotton  fibre  or  staple  from  its  seed  —  hitherto 
laboriously  done  by  hand.  Applied  chemistry  also  began  to 
appear,  e.g.  in  the  manufacture  of  illuminating  gas  by  Murdoch 
at  Salford,  England,  in  1792,  while  the  discoveries  of  Galvani  and 
Volta  at  the  very  end  of  the  century  opened  up  that  new  era 
of  electricity  in  the  midst  of  which  we  dwell  to-day. 

THE  INFLUENCE  OF  SCIENCE  UPON  THE  SPIRIT  OF  THE  EIGH- 
TEENTH CENTURY.  —  Writers  on  the  literature  of  the  eighteenth 
century,  after  condemning  it  because  of  its  comparative  barrenness 
in  great  works  of  art  or  literature,  are  apt  to  find  the  reason  in  one 
or  another  aspect  of  the  growth  of  science.  Professor  Dowden,  for 
example,  in  his  essay  on  Goethe,  remarks  that 

Rousseau's  emancipation  of  the  heart,  was  felt  in  the  eighteenth 
century  to  be  a  blessed  deliverance  from  the  eager,  yet  too  arid, 
speculation  of  the  age, 

although  he  admits  that :  — 

Humanity,  as  Voltaire  said,  had  lost  its  title-deeds,  and  the  task 
of  the  eighteenth  century  was  to  recover  them. 

Dowden's  unusually  charitable  judgment  of  the  century  is  more 
or  less  typical  of  literary  opinion  generally. 

For  the  scientist,  on  the  other  hand,  few  centuries  in  all  history 
are  more  important,  for  the  eighteenth  was  not  only  rich  in  scien- 
tific performance  but  still  more  pregnant  with  promise.  And 
even  in  art  —  if  in  that  term  music  be  included  —  and  literature, 
a  century  which  produced  a  Haydn,  a  Mozart  and  a  Beethoven, 
with  a  Burns,  a  Voltaire,  a  Wordsworth  and  a  Goethe,  need  not 
fear  to  hold  up  its  head. 

We  have  mentioned  above  the  first  School  of  Mines :  viz.  that 
at  Freiberg,  in  Saxony  (1765).  The  first  School  of  Civil  Engineer- 
ing was  established  in  Paris  (1747).  In  this  century  also  were 
established  new  universities,  e.g.,  Yale  (1701),  Gottingen  (1737), 
Princeton  (1746),  Bonn  (1777)  and  Brussels  (1781). 


322  A  SHORT  HISTORY  OF  SCIENCE 

The  "physiocrats"  and  the  "encyclopaedists"  of  the  French 
school  of  practical  philosophers  also  deserve  notice,  for  they  were 
professedly  inspired  by  science  and  seeking  to  apply  it  to  human 
society.  Even  in  so  humble  a  pursuit  as  the  attempt  to  overcome 
in  time  of  famine  the  prejudices  of  the  populace  against  the  potato, 
Turgot  and  his  fellows  did  good  work  for  applied  science.  Nor 
should  we  forget  the  service  to  social  science  of  Count  Rumford, 
who  for  the  first  time  grappled  boldly  with  problems  as  far  apart 
as  the  control  of  mendicity,  of  smoky  chimneys,  and  of  poverty. 
Much  of  Rumford's  best  work,  though  done  in  the  nineteenth 
century,  had  its  origin  in  the  scientific  spirit  and  achievements  of 
the  eighteenth. 

As  the  century  drew  to  its  close,  an  English  physician,  Edward 
Jenner,  by  the  use  of  the  basic  methods  of  inductive  scientific 
research  —  accurate  observation,  skillful  experimentation,  careful 
generalization  and  thorough  verification — created  a  new  science, 
preventive  medicine,  and  conferred  upon  mankind  the  priceless 
blessings  of  vaccination.  (See  Appendix  G.) 

The  nebular  hypothesis  of  Laplace,  through  its  central  idea  of 
natural  development  rather  than  sudden  and  special  (artificial) 
creation  of  the  solar  system,  was  an  important  preparation  of 
men's  minds  for  theories  of  transformation  or  evolution.  Button's 
Theory  of  the  Earth  enforced  the  same  idea  for  the  familiar  earth, 
while  the  metamorphoses  of  the  parts  of  the  flower,  pointed  out  by 
Goethe,  helped  to  pave  the  way  for  acceptance  of  the  idea  of 
gradual  modification  of  organs  and  even  of  organisms  into  others. 
To  these  matters  we  shall  return  in  our  discussion  of  Evolution 
in  the  final  chapter. 

REFERENCES  FOR  READING 
(See  page  461.) 


CHAPTER  XV 
MODERN   TENDENCIES   IN   MATHEMATICAL   SCIENCE 

Mathematics  is  the  queen  of  the  sciences  and  arithmetic  the 
queen  of  mathematics.  She  often  condescends  to  render  service  to 
astronomy  and  other  natural  sciences,  but  in  all  relations  she  is  en- 
titled to  the  first  rank.  —  Gauss. 

Thought-economy  is  most  highly  developed  in  mathematics,  that 
science  which  has  reached  the  highest  formal  development,  and  on 
which  natural  science  so  frequently  calls  for  assistance.  Strange  as 
it  may  seem,  the  strength  of  mathematics  lies  in  the  avoidance  of  all 
unnecessary  thoughts,  in  the  utmost  economy  of  thought-operations. 
The  symbols  of  order,  which  we  call  numbers,  form  already  a  system 
of  wonderful  simplicity  and  economy.  When  in  the  multiplication 
of  a  number  with  several  digits  we  employ  the  multiplication  table 
and  thus  make  use  of  previously  accomplished  results  rather  than 
repeat  them  each  time,  when  by  the  use  of  tables  of  logarithms  we 
avoid  new  numerical  calculations  by  replacing  them  by  others  long 
since  performed,  when  we  employ  determinants  instead  of  carrying 
through  from  the  beginning  the  solution  of  a  system  of  equations, 
when  we  decompose  new  integral  expressions  into  others  that  are 
familiar,  —  we  see  in  all  this  but  a  faint  reflection  of  the  intellectual 
activity  of  a  Lagrange  or  Cauchy,  who  with  the  keen  discernment  of 
a  military  commander  marshals  a  whole  troop  of  completed  operations 
in  the  execution  of  a  new  one.  —  Mack. 

The  iron  labor  of  conscious  logical  reasoning  demands  great  per- 
severance and  great  caution ;  it  moves  on  but  slowly,  and  is  rarely 
illuminated  by  brilliant  flashes  of  genius.  It  knows  little  of  that 
facility  with  which  the  most  varied  instances  come  thronging  into 
the  memory  of  the  philologist  or  historian.  Rather  is  it  an. essential 
condition  of  the  methodical  progress  of  mathematical  reasoning  that 
the  mind  should  remain  concentrated  on  a  single  point,  undisturbed 
alike  by  collateral  ideas  on  the  one  hand,  and  by  wishes  and  hopes  on 

323 


324  A  SHORT  HISTORY  OF  SCIENCE 

the  other,  and  moving  on  steadily  in  the  direction  it  has  deliberately 
chosen.  —  Helmholtz. 

Nature  herself  exhibits  to  us  measurable  and  observable  quan- 
tities in  definite  mathematical  dependence;  the  conception  of  a 
function  is  suggested  by  all  the  processes  of  nature  where  we  observe 
natural  phenomena  varying  according  to  distance  or  to  time.  Nearly 
all  the  "known"  functions  have  presented  themselves  in  the  attempt 
to  solve  geometrical,  mechanical,  or  physical  problems.  —  Merz. 

We  have  now  reached  a  period  of  maturity  in  the  evolution  of 
mathematical  science  beyond  which  any  attempt  to  follow  its 
details  would  involve  technical  discussions  outside  the  range  of 
this  work.  The  present  chapter  will  be  devoted  to  a  general 
survey  of  modern  tendencies  in  pure  and  applied  mathematics, 
in  mechanics,  in  mathematical  physics  and  in  astronomy.  The 
most  notable  single  fact  in  the  centuries  under  discussion  is  the 
increasing  specialization  resulting  from  the  great  expansion  of 
scientific  knowledge.  It  is  no  longer  possible  for  the  individual 
scholar  to  command  the  range  at  once  of  philosophy,  mathe- 
matics, physics,  chemistry,  and  the  natural  sciences.  It  has  even 
become  more  and  more  difficult  to  have  a  general  knowledge  of 
any  one  of  these  broad  fields. 

MATHEMATICS  AND  MECHANICS  IN  THE  EIGHTEENTH  CENTURY. 
—  The  invention  of  the  infinitesimal  calculus  by  Newton  and 
Leibnitz  was  comparable  in  its  relations  and  consequences  with 
the  discovery  of  a  new  world  by  Columbus  two  centuries  earlier. 
As  in  that  case  the  discovery  was  not  an  absolutely  sudden  one ; 
other  explorers  had  hoped  or  imagined,  but  only  genius  of  that 
highest  order  which  we  call  inspired,  gained  the  complete  revela- 
tion. The  years  next  following  the  great  discovery  were  natu- 
rally a  period  of  eager  and  wide-ranging  exploration,  of  optimistic 
self-confident  pioneering.  Such  was  the  power  of  the  new  method, 
that  one  might  rashly  hope  no  secret  of  nature  could  long  resist 
its  attack.  As  circumnavigation  of  the  globe  was  not  long  in 
following  the  discovery  of  America,  so  the  cycle  of  mathematical 
knowledge  might  be  completed.  The  parallel  has  failed.  The 
calculus  grew  out  of  the  insistent  grappling  by  mathematicians  with 


TENDENCIES    IN    MATHEMATICAL    SCIENCE       325 

problems  which  had  defied  the  feebler  tools  of  the  earlier  mathe- 
matics. One  obstacle  after  another  has  been  gradually  sur- 
mounted by  the  invention  of  new  and  more  powerful  methods  of 
ever  increasing  generality,  just  as  increasingly  powerful  telescopes 
have  revealed  unnumbered  new  suns ;  and  no  boundary  or  limit 
to  this  evolutionary  progress  can  be  foreseen  or  imagined.  On 
the  other  hand,  as  the  new  world  has  been  gradually  settled, 
civilized,  and  cultivated,  so  the  fields  of  mathematics  which  were 
opened  up  in  the  eighteenth  century  have  been  critically  ex- 
amined in  the  nineteenth,  with  much  revision  of  fundamentals. 

The  main  features  of  eighteenth  century  mathematics  were: 
—  the  working  out  of  the  differential  and  integral  calculus  into 
substantially  the  form  they  have  ever  since  retained ;  the  begin- 
nings of  differential  equations  as  a  natural  outgrowth  of  integral 
calculus,  and  the  beginnings  of  the  calculus  of  variations;  the 
systematic  application  of  the  new  ideas  to  mechanics,  and  in  par- 
ticular to  celestial  mechanics.  The  century  was  also  notable  for 
important  discoveries  in  astronomy  and  physics,  including  for  ex- 
ample that  of  the  aberration  of  light ;  a  vigorous  attack  on  "  the 
problem  of  three  bodies  "  ;  and  the  earlier  telescopic  work  of  the 
Herschels,  culminating  in  the  discovery  of  a  new  planet,  Uranus. 

Among  the  leading  mathematicians  of  the  period  were  Mac- 
laurin  of  Scotland,  various  members  of  the  Swiss  Bernoulli  family, 
Euler  also  a  native  of  Switzerland,  Lagrange  of  Italy,  and  in 
France,  Clairaut,  d'Alembert,  and  Laplace.  In  spite  of  the  unique 
supremacy  of  Newton,  the  absence  of  Britons  from  this  list  is 
notable.  The  bitter  personal  controversy  between  Newton's  ad- 
herents and  those  of  Leibnitz  produced  or  aggravated  an  un- 
fortunate division  between  the  English  and  the  continental 
mathematicians.  For  the  former,  persistence  in  Newton's  in- 
ferior notation  became  a  matter  of  national  pride,  and  progress 
was  correspondingly  retarded.  Of  the  mathematicians  named 
above,  the  Bernoullis  and  Euler  on  the  continent  and  Maclaurin 
in  Scotland  bore  a  leading  part  in  the  systematization  of  the 
calculus,  while  Lagrange  and  Laplace  were  preeminent  in  the 
development  of  analytical  and  celestial  mechanics  respectively. 


326  A  SHORT  HISTORY  OF  SCIENCE 

Maclaurin's  (1698-1746)  Treatise  of  Fluxions  (1742)  was  "  the 
first  logical  and  systematic  exposition  of  the  method  of  fluxions," 
and  the  applications  to  problems  contained  in  it  were  characterized 
by  Lagrange  as  the  "masterpiece  of  geometry,  comparable  with 
the  finest  and  most  ingenious  work  of  Archimedes."  Maclaurin's 
point  of  view  may  be  illustrated  by  the  following  passage :  — 

Magnitudes  were  supposed  to  be  generated  by  motion;  and,  by 
comparing  the  increments  that  were  generated  in  any  equal  successive 
parts  of  the  time,  it  was  first  determined  whether  the  motion  was  uni- 
form, accelerated,  or  retarded.  .  .  .  When  the  motion  was  accelerated, 
this  increment  was  resolved  into  two  parts ;  that  which  alone  would 
have  been  generated  if  the  motion  had  not  been  accelerated,  but  had 
continued  uniform  from  the  beginning  of  the  time,  and  that  which  was 
generated  in  consequence  of  the  continual  acceleration  of  the  motion 
during  that  time.  The  latter  part  was  rejected,  and  the  former  only 
retained  for  measuring  the  motion  at  the  beginning  of  the  time. 
And  in  like  manner,  when  the  motion  was  retarded,  ...  so  that  the 
motion  at  the  time  proposed  was  accurately  measured,  and  the  ratio 
of  the  fluxions  always  accurately  represented.  In  the  method  of 
infinitesimals,  the  element,  by  which  any  quantity  increases  or  de- 
creases, is  supposed  to  be  infinitely  small,  and  is  generally  expressed 
by  two  or  more  terms,  some  of  which  are  infinitely  less  than  the  rest, 
which  being  neglected  as  of  no  importance,  the  remaining  terms  form 
what  is  called  the  difference  of  the  proposed  quantity.  The  terms 
that  are  neglected  in  this  manner,  as  infinitely  less  than  the  other 
terms  of  the  element,  are  the  very  same  which  arise  in  consequence 
of  the  acceleration,  or  retardation,  of  the  generating  motion,  during 
the  infinitely  small  time  in  which  the  element  is  generated.  .  .  .  The 
conclusions  are  accurately  true,  without  even  an  infinitely  small 
error.  .  .  . 

Daniel  Bernoulli  (1700-1782)  made  such  good  use  of  the  new 
mathematical  methods  in  attacking  previously  unsolved  problems 
of  mechanics,  that  he  has  been  called  the  founder  of  mathematical 
physics.  He  recognized  the  importance  of  the  principle  of  the 
conservation  of  force  anticipated  in  part  by  Huygens. 

Euler  (1707-1783),  while  Swiss  by  birth,  spent  most  of  his  life 


TENDENCIES  IN  MATHEMATICAL  SCIENCE        327 

at  the  courts  of  St.  Petersburg  and  Berlin.  In  spite  of  partial 
and  ultimately  complete  blindness,  his  scientific  productivity  was 
enormous,  and  one  of  the  most  ambitious  scientific  undertakings 
of  our  own  time  is  the  publication  of  his  complete  works  in  45 
volumes,  by  international  cooperation.  Our  college  mathematics 
—  algebra,  analytic  geometry,  and  the  calculus  —  owes  its  pres- 
ent shape  largely  to  his  works. 

Euler's  Complete  Introduction  to  Algebra  was  one  of  the  most 
influential  books  on  algebra  in  the  eighteenth  century,  and  not  the 
least  because  it  is  written  with  extraordinary  clearness  and  in  easily 
intelligible  form.  Euler  was  at  that  time  already  totally  blind.  He 
picked  out  a  young  man  whom  he  had  brought  with  him  from  Berlin 
as  an  attendant  and  who  could  reckon  tolerably,  but  who  otherwise 
had  no  understanding  of  mathematics.  He  was  a  tailor  by  trade 
and  of  moderate  intellectual  capacity.  To  him  Euler  dictated  this 
book,  and  the  amanuensis  not  only  understood  everything  well  but 
in  a  short  time  acquired  the  power  to  carry  out  difficult  algebraic 
processes  by  himself  with  much  facility.  It  was  this  book  which 
completing  the  development  begun  by  Vieta  made  algebra  an  inter- 
national mathematical  shorthand. 

Euler  formulated  the  idea  of  function  which  has  proved  so  fun- 
damental in  modern  mathematics,  both  pure  and  applied.  His 
work  also  contains  the  first  systematic  treatment  of  the  calculus 
of  variations,  which  is  defined  as  "the  method  of  finding  the 
change  caused  in  an  expression  containing  any  number  of  variables 
when  one  lets  all  or  any  of  the  variables  change"  or  more  geo- 
metrically "  a  method  of  finding  curves  having  a  particular  prop- 
erty in  the  highest  or  the  lowest  degree." 

In  other  fields  Euler  "  was  the  first  to  treat  the  vibrations  of  light 
analytically  and  to  deduce  the  equation  of  the  curve  of  vibration  as 
dependent  upon  elasticity  and  density.  ...  He  deduced  the  law  of 
refraction  analytically  and  explained  that  the  rays  of  greater  wave- 
length must  suffer  the  least  deviation.  .  .  .  He  studied  dispersion 
in  the  search  for  a  corrective  for  chromatic  aberration,  which  Newton 
had  declared  unattainable.  ...  It  was  this  investigation  that  in- 


328  A  SHORT  HISTORY  OF  SCIENCE 

duced  Dolland  to  construct  his  achromatic  lenses.  .  .  .  Euler  was 
thus  the  only  physicist  of  the  eighteenth  century  who  advanced  the 
undulatory  theory."  —  Bull.  Amer.  Math.  Soc.,  Dec.,  1907. 

Euler  gained  a  share  of  the  prize  of  £20,000  offered  by  the 
British  parliament  for  a  method  of  determining  longitude  at 
sea,  half  of  the  same  prize  falling  to  Harrison  the  maker  of  a  ship's 
chronometer  sufficiently  accurate  for  the  same  purpose. 

He  was  probably  the  most  versatile  as  well  as  the  most  prolific 
of  mathematicians  of  all  time.  There  is  scarcely  any  branch  of 
modern  analysis  to  which  he  was  not  a  large  contributor,  and  his 
extraordinary  powers  of  devising  and  applying  methods  of  calculation 
were  employed  by  him  with  great  success  in  each  of  the  existing 
branches  of  applied  mathematics;  problems  of  abstract  dynamics, 
of  optics,  of  the  motion  of  fluids,  and  of  astronomy  were  all  in  turn 
subjected  to  his  analysis  and  solved.  —  Berry. 

It  is  the  invaluable  merit  of  the  great  Basle  mathematician 
Leonhard  Euler,  to  have  freed  the  analytical  calculus  from  all  geo- 
metrical bonds,  and  thus  to  have  established  analysis  as  an  inde- 
pendent science,  which  from  his  time  on  has  maintained  an  unchal- 
lenged leadership  in  the  field  of  mathematics.  —  Hankel. 

PROGRESS  IN  THEORETICAL  MECHANICS.  The  rapid  develop- 
ment of  mechanics  in  the  eighteenth  century  culminated  in  the 
great  classical  treatises  of  d'Alembert  (1717-1783)  —  Traite  de 
dynamique  —  and  Lagrange  (1736-1813) — Mecanique  analytique, 
systematizing  and  coordinating  the  theories  and  results  thus  far 
obtained.  D'Alembert,  working  out  ideas  based  on  Huy gens' 
theory  of  the  centre  of  oscillation,  formulated  a  very  general  dy- 
namical principle  since  known  under  his  name :  — 

On  a  system  of  points  M,  M',  M"  ...  connected  with  one 
another  in  any  way,  the  forces  P,  P',  P"  ...  are  impressed.  These 
forces  would  impart  to  the  free  points  of  the  system  certain  deter- 
minate motions.  To  the  connected  points,  however,  different  motions 
are  usually  imparted  —  motions  which  could  be  produced  by  the  forces 
Wt  W,  W"  ...  These  last  are  the  motions  which  we  shall  study. 

Conceive  the  force  P  resolved  into  W  and  V,  the  force  P'  into  W 
and  V,  and  the  force  P"  into  W"  and  V",  and  so  on.  Since,  owing 


TENDENCIES  IN  MATHEMATICAL  SCIENCE         329 

to  the  connections,  only  the  components  W,  W,  W"  ...  are  effec- 
tive, therefore  the  forces  F,  V,  V"  ...  must  be  equilibrated  by  the 
connections.  We  will  call  the  forces  P,  P',  P"  ...  the  impressed 
forces,  the  forces  W,  W,  W"  ...,  which  produce  the  actual  motions, 
the  effective  forces,  and  the  forces  F,  F',  V"  ...  the  forces  gained,  and 
lost,  or  the  equilibrated  forces.  We  perceive,  thus,  that  if  we  resolve 
the  impressed  forces  into  the  effective  forces  and  the  equilibrated 
forces,  the  latter  form  a  system  balanced  by  the  connections.  —  Mach. 

To  d'Alembert  is  attributed  the  celebrated  epigram  concerning 
Benjamin  Franklin,  "He  snatched  the  thunderbolt  from  heaven, 
the  sceptre  from  tyrants"  (Eripuit  coelo  fulmen  sceptrumque 
tyrannis] . 

J.  L.  Lagrange  (1736-1813),  a  native  of  Turin,  also  spent  many 
years  in  Berlin  and  his  later  life  in  Paris,  where  he  became  pro- 
fessor at  the  newly  established  Ecole  poly  technique.  At  the 
age  of  25  he  was  pronounced  the  greatest  mathematician  living. 
His  chief  work,  the  Mecanique  analytique,  is  a  masterly  discussion 
of  the  whole  subject,  showing  by  the  aid  of  the  new  mathematical 
methods  its  dependence  on  a  few  fundamental  principles.  On  the 
death  of  his  royal  patron,  Frederick  the  Great,  in  1787,  he  was 
invited  from  Berlin  not  only  to  Paris,  but  to  Spain  and  to  Naples, 
accepting  the  first-named  opportunity.  Lagrange's  works  include 
also  very  important  contributions  to  differential  equations  and 
the  calculus  of  variations^  of  which  any  detailed  account  would 
be  too  technical  for  our  purpose.  The  significance  and  impor- 
tance of  Lagrange's  Mecanique  analytique  are  within  its  field  com- 
parable with  those  of  Newton's  Principia. 

Lagrange  like  Newton  has  possessed  in  the  highest  degree  the  fortu- 
nate art  of  discovering  the  universal  principles  which  constitute  the 
essence  of  science.  This  art  he  understands  how  to  unite  with  a  rare 
elegance  in  the  development  of  the  most  abstruse  theories.  —  Laplace. 

In  contrast  with  the  predominantly  geometrical  and  synthetic 
methods  of  Newton,  Lagrange's  methods  are  mainly  analytical. 

Generality  of  points  of  view  and  of  methods,  precision  and  ele- 
gance in  presentation,  have  become,  since  Lagrange,  the  common 


330  A  SHORT  HISTORY  OF  SCIENCE 

property  of  all  who  would  lay  claim  to  the  rank  of  scientific  mathe- 
maticians. —  Hankel. 

When  we  have  grasped  the  spirit  of  the  infinitesimal  method, 
and  have  verified  the  exactness  of  its  results  either  by  the  geometrical 
method  of  prime  and  ultimate  ratios,  or  by  the  analytical  method  of 
derived  functions,  we  may  employ  infinitely  small  quantities  as  a  sure 
and  valuable  means  of  shortening  and  simplifying  our  proofs. 

—  Lagrange. 

Lagrange  also  applied  his  great  powers  of  analysis  to  problems 
in  astronomy  and  in  cartography. 

CELESTIAL  MECHANICS.  —  Pierre  Simon  Laplace  (1749-1827) 
was  of  humble  Norman  antecedents  which  he  in  later  life  somewhat 
disdained,  and  played  a  great  part  in  the  scientific  activity  under 
Napoleon.  In  the  five  volumes  of  his  Mecanique  celeste,  he  pro- 
duced a  permanent  monument  to  his  own  genius.  It  was  his  lofty 
ambition 

to  offer  a  complete  solution  of  the  great  mechanical  problem  pre- 
sented by  the  solar  system,  and  bring  theory  to  coincide  so  closely 
with  observation  that  empirical  equations  should  no  longer  find  a 
place  in  astronomical  tables. 

He  regarded  analysis  merely  as  a  means  of  attacking  physical  prob- 
lems, though  the  ability  with  which  he  invented  the  necessary  anal- 
ysis is  almost  phenomenal.  As  long  as  his  results  were  true  he  took 
very  little  trouble  to  explain  the  steps  by  which  he  arrived  at  them ; 
he  never  studied  elegance  or  symmetry  in  his  processes,  and  it  was 
sufficient  for  him  if  he  could  by  any  means  solve  the  particular  ques- 
tion he  was  discussing.  —  Ball. 

Bowditch,  the  American  translator  of  his  great  work,  remarks 
significantly :  — 

I  never  come  across  one  of  Laplace's  '  Thus  it  plainly  appears '  without 
feeling  sure  that  I  have  hours  of  hard  work  before  me  to  fill  up  the 
chasm  and  find  out  and  show  how  it  plainly  appears. 

In  the  words  of  the  historian  Tod  hunter, 

a  complete  evolution  of  the  history  will  restore  the  reputation  of  La- 
place to  its  just  eminence.  The  advance  of  mathematical  science  is 


TENDENCIES  IN  MATHEMATICAL  SCIENCE        331 

on  the  whole  remarkably  gradual,  for  with  the  single  exception  of 
Newton  there  is  very  little  exhibition  of  great  and  sudden  develop- 
ments ;  but  the  possessions  of  one  generation  are  received,  augmented 
and  transmitted  by  the  next.  It  may  be  confidently  maintained  that  no 
single  person  has  contributed  more  to  the  general  stock  than  Laplace. 

THE  PERTURBATION  PROBLEM.  —  Newton  had  worked  out  the 
theory  of  a  single  planet  or  satellite  revolving  about  its  primary. 
The  consequent  discrepancies  were  held  by  some  to  indicate 
inexactness  in  his  hypothetical  laws.  Laplace  occupied  himself 
with  a  thorough  study  of  the  great  problem  of  three  bodies,1  and 
without  fully  solving  it,  accounted  to  a  great  extent  for  the  dis- 
crepancies in  question.  In  particular  he  maintained  the  stability 
of  the  solar  system.  His  Mecanique  celeste  has  been  charac- 
terized as  an  infinitely  extended  and  enriched  edition  of  Newton's 
Principia. 

In  his  confidence  in  the  extending  range  of  mathematical  methods 
Laplace  says :  — 

Given  for  one  instant  an  intelligence  which  could  comprehend  all 
the  forces  by  which  nature  is  animated  and  the  respective  positions  of 
the  beings  which  compose  it,  if  moreover  this  intelligence  were  vast 
enough  to  submit  these  data  to  analysis,  it  would  embrace  in  the  same 
formula  both  the  movements  of  the  largest  bodies  in  the  universe 
and  those  of  the  lightest  atom  :  to  it  nothing  would  be  uncertain,  and 
the  future  as  the  past  would  be  present  to  its  eyes.  The  human  mind 
offers  a  feeble  outline  of  that  intelligence,  in  the  perfection  which  it 
has  given  to  astronomy.  Its  discoveries  in  mechanics  and  in  geom- 
etry, joined  to  that  of  universal  gravity,  have  enabled  it  to  com- 
prehend in  the  same  analytical  expressions  the  past  and  future  states 
of  the  world  system. 

THE  NEBULAR  HYPOTHESIS.  —  In  his  Exposition  du  systeme 
du  monde,  "one  of  the  most  perfect  and  charmingly  written 

^Given  at  any  time  the  positions  and  motions  of  three  mutually  gravitating 
bodies,  to  determine  their  positions  and  motions  at  any  other  time  —  a  particular 
case  of  the  actual  more  general  problem :  Given  the  18  known  bodies  of  the  solar 
system,  and  their  positions  and  motions  at  any  time,  to  deduce  from  their  mutual 
gravitation  by  a  process  of  mathematical  calculation  their  positions  and  motions 
at  any  other  time ;  and  to  show  that  these  agree  with  those  actually  observed. 


332  A  SHORT  HISTORY  OF  SCIENCE 

popular  treatises  on  astronomy  ever  published,  in  which  the  great 
mathematician  never  uses  either  an  algebraical  formula  or  a 
geometrical  diagram",  Laplace  presents  the  arguments  for  his 
nebular  hypothesis  along  the  following  general  lines:  — 

In  spite  of  the  separation  of  the  planets  they  bear  certain  re- 
markable relations  to  each  other ; 

All  the  planets  travel  about  the  sun  in  the  same  direction  and 
almost  in  the  same  plane ; 

The  satellites  also  travel  about  their  planets  in  this  same 
direction  and  almost  in  the  same  plane ; 

Finally,  sun,  planets  and  satellites  revolve  in  the  same  sense 
about  their  own  axes  and  this  rotation  is  approximately  in  the 
orbital  plane. 

These  agreements  cannot  be  accidental.  Laplace  seeks  the 
cause  in  the  existence  of  an  original  vast  nebulous  mass  forming 
a  sort  of  atmosphere  about  the  sun  and  extending  beyond  the 
outermost  planet.  Initial  or  acquired  rotation  of  the  nebula  at- 
tended by  gradual  cooling  and  contraction  has  caused  the  cen- 
trifugal separation  of  masses  analogous  to  Saturn's  rings,  out  of 
which  planets  have  gradually  condensed,  throwing  off  their  own 
satellites  in  the  process.  This  hypothesis  had  already  been 
proposed  in  substance  by  Kant  in  1755.  Its  later  history  will 
be  touched  on  in  a  following  chapter. 

Laplace  was  also  deeply  interested  in  the  theory  of  probability, 
as  may  be  illustrated  by  the  following  passages :  — 

The  most  important  questions  of  life  are,  for  the  most  part,  really 
only  problems  of  probability.  Strictly  speaking  one  may  even  say 
that  nearly  all  our  knowledge  is  problematical;  and  in  the  small 
number  of  things  which  we  are  able  to  know  with  certainty,  even  in 
the  mathematical  sciences  themselves,  induction  and  analogy,  the 
principal  means  for  discovering  truth,  are  based  on  probabilities,  so 
that  the  entire  system  of  human  knowledge  is  connected  with  this 
theory. 

It  is  remarkable  that  a  science  (probabilities)  which  began  with 
the  consideration  of  games  of  chance,  should  have  become  the  most 
important  object  of  human  knowledge. 


TENDENCIES  IN  MATHEMATICAL  SCIENCE        333 

The  theory  of  probabilities  is  at  bottom  nothing  but  common 
sense  reduced  to  calculus ;  it  enables  us  to  appreciate  with  exactness 
that  which  accurate  minds  feel  with  a  sort  of  instinct  for  which  oft- 
times  they  are  unable  to  account.  If  we  consider  the  analytical 
methods  to  which  this  theory  has  given  birth,  the  truth  of  the  prin- 
ciples on  which  it  is  based,  the  fine  and  delicate  logic  which  their  em- 
ployment in  the  solution  of  problems  requires,  the  public  utilities 
whose  establishment  rests  upon  it,  the  extension  which  it  has  received 
and  which  it  may  still  receive  through  its  application  to  the  most 
important  problems  of  natural  philosophy  and  the  moral  sciences; 
if  again  we  observe  that,  even  in  matters  which  cannot  be  submitted 
to  the  calculus,  it  gives  us  the  surest  suggestions  for  the  guidance  of 
our  judgments,  and  that  it  teaches  us  to  avoid  the  illusions  which 
often  mislead  us,  then  we  shall  see  that  there  is  no  science  more  worthy 
of  our  contemplations  nor  a  more  useful  one  for  admission  to  our 
system  of  public  education. 

MODERN  ASTRONOMY.  TELESCOPIC  DISCOVERIES.  —  The  im- 
mense impetus  given  to  astronomy  by  the  revolutionary  discov- 
eries of  Copernicus,  Tycho  Brahe,  Galileo,  Kepler,  and  Newton, 
followed  in  the  eighteenth  century  by  the  complete  working  out  of 
the  mathematical  consequences  of  the  gravitation  theory  by  Laplace 
and  others,  placed  the  science  in  advance  of  all  its  rivals  and 
seemed  to  make  it  a  model  for  their  imitation. 

A  different  and  most  far-reaching  tendency  appears  with  the 
work  of  the  Herschels.  Friedrich  Wilhelm  Herschel  (1738-1822), 
a  poor  German  musician  emigrating  to  England  and  devoting  his 
spare  time  unremittingly  to  astronomy,  with  the  help  of  his  capable 
sister  laid  the  foundations  of  modern  physical  astronomy.  In  1781 
he  amazed  himself  as  well  as  the  scientific  world  by  discovering  be- 
yond Saturn  a  new  planet,  Uranus,  —  taking  it  at  first  for  a 
comet.  Constructing  more  and  more  powerful  telescopes  he  dis- 
covered several  satellites  of  Uranus  and  two  of  Saturn.  He  also 
determined  a  motion  of  the  solar  system  as  a  whole,  towards  a 
point  in  the  constellation  Hercules.  He  catalogued  more  than 
800  double  stars  and  more  than  2000  nebulas,  recognizing  among 
the  latter,  as  he  believed,  different  stages  of  the  evolution  of  other 
planetary  systems.  He  observes : 


334  A  SHORT  HISTORY  OF  SCIENCE 

This  method  of  viewing  the  heavens  seems  to  throw  them  into 
a  new  kind  of  light.  They  are  now  seen  to  resemble  a  luxuriant 
garden,  which  contains  the  greatest  variety  of  productions,  in  different 
flourishing  beds ;  and  one  advantage  we  may  at  least  reap  from  it  is, 
that  we  can,  as  it  were,  extend  the  range  of  our  experience  to  an  im- 
mense duration.  For,  to  continue  the  simile  I  have  borrowed  from 
the  vegetable  kingdom,  is  it  not  almost  the  same  thing,  whether  we 
live  successively  to  witness  the  germination,  blooming,  foliage,  fecun- 
dity, fading,  withering,  and  corruption  of  a  plant,  or  whether  a  vast 
number  of  specimens  selected  from  every  stage  through  which  the  plant 
passes  in  the  course  of  its  existence,  be  brought  at  once  to  our  view  ? 

With  a  reminiscence  of  Descartes,  he  says :  — 

I  determined  to  accept  nothing  on  faith,  but  to  see  with  my  own 
eyes  what  others  had  seen  before  me.  .  .  .  When  I  had  carefully 
and  thoroughly  perfected  the  great  instrument  in  all  its  parts  I 
made  systematic  use  of  it  in  my  observations  of  the  heavens,  first 
forming  a  determination  never  to  pass  by  any,  the  smallest,  portion 
of  them  without  due  investigation. 

To  the  eighteenth  century  also  belong  elaborate  and  costly 
expeditions  —  including  one  organized  by  the  American  Philosoph- 
ical Society  of  Philadelphia  —  to  observe  transits  of  Venus,  as  a 
means  for  determining  the  distance  from  the  sun  to  the  earth. 

MATHEMATICAL  PROGRESS  AND  PHYSICAL  SCIENCE. — Besides 
the  extension  of  mathematical  ideas  and  methods  to  mechanics, 
astronomy,  optics  and  other  branches  of  physics,  chemistry  was 
now  also  becoming  a  quantitative  science.  So  Scheele  begins  a 
work  published  in  1777 :  — 

To  resolve  bodies  skilfully  into  their  components,  to  discover  their 
properties  and  to  combine  them  in  different  ways,  is  the  chief  pur- 
pose of  chemistry. 

Richter,  in  his  Stoichiometry  (1792-1802),  even  speaks  of 
chemistry  as  a  branch  of  applied  mathematics.  Already  the 
pioneer  Robert  Boyle  had  written :  — 

I  confess,  that  after  I  began  ...  to  discern  how  useful  mathe- 
maticks  may  be  made  to  physicks,  I  have  often  wished  that  I  had 


TENDENCIES  IN  MATHEMATICAL  SCIENCE        335 

employed  about  the  speculative  part  of  geometry,  and  the  cultivation 
of  the  specious  Algebra  I  had  been  taught  very  young,  a  good  part 
of  that  time  and  industry  that  I  had  spent  about  surveying  and  forti- 
fication (of  which  I  remember  I  once  wrote  an  entire  treatise)  and 
other  parts  of  practick  mathematicks. 

Mathematicks  may  help  the  naturalists,  both  to  frame  hypotheses, 
and  to  judge  of  those  that  are  proposed  to  them,  especially  such  as 
relate  to  mathematical  subjects  in  conjunction  with  others. 

Even  in  natural  science  Stephen  Hales  says  in  1727 :  — 

And  since  we  are  assured  that  the  all-wise  Creator  has  observed 
the  most  exact  proportions,  of  number,  weight  and  measure,  in  the 
make  of  all  things ;  the  most  likely  way  therefore  to  get  any  insight 
into  the  nature  of  these  parts  of  the  creation,  must  in  all  reason  be 
to  number,  weigh  and  measure.  And  we  have  much  encourage- 
ment to  pursue  this  method,  of  searching  into  the  nature  of  things, 
from  the  great  success  that  has  attended  any  attempts  of  this 
kind. 

Summing  up  these  tendencies,  a  recent  writer  remarks :  -. — 

In  the  eighteenth  century  mathematics  was  regarded  by  many 
scholars  as  the  ideal,  the  completeness  and  exactness  of  whose  methods 
should  be  arrived  at  by  other  less  highly  developed  branches.  So 
Laplace's  popularized  version  of  his  celestial  mechanics  met  an  eager 
need,  and  even  Voltaire  undertook  the  championship  of  the  Newtonian 
philosophy.  Logic  and  even  ethics  were  drawn  into  the  mathematical 
retinue.  For  Maupertuis  the  good  is  a  positive  quantity,  the  bad  a 
negative.  Joys  and  griefs  make  up  human  life  according  to  the  laws 
of  algebraic  addition,  and  it  is  the  business  of  statesmen  to  see  that  the 
positive  balance  is  as  large  as  possible.  The  great  Buffon  adds  to  his 
natural  history  a  supplement  on  moral  arithmetic.  Mathematics 
aims  at  the  leadership  both  in  natural  science  and  in  human  affairs. 

In  spite  of  this  perhaps  exaggerated  predilection  in  learned 
and  polite  society,  educational  curricula  remained  weak  and 
conservative.  Powerful  progressive  tendencies  growing  out  of 
the  French  Revolution  found  expression  in  the  founding  of  the 
Ecole  polytechnique,  —  under  the  leadership  of  Monge,  —  which 
has  ever  since  been  an  important  centre  of  mathematical  activity. 


336  A  SHORT  HISTORY  OF  SCIENCE 

Its  curriculum  included,  in  the  first  year,  analytic  geometry  of 
space  and  descriptive  geometry,  in  the  second,  mechanics  of 
solids  and  liquids,  in  the  third,  theory  of  mechanics. 

Reviewing  eighteenth  century  mathematics,  a  recent  German 
writer  says :  — 

In  the  science  itself  there  showed  itself  with  the  close  of  the 
eighteenth  century  a  certain  exhaustion.  'The  mine  is,  it  seems  to 
me,  too  deep/  wrote  Lagrange  in  the  year  1781  to  d'Alembert,  'and 
unless  new  veins  are  discovered  it  must  sooner  or  later  be  abandoned/ 
In  the  nineteenth  century  men  have  dug  deeper  and  struck  noble 
ores,  but  serious  obstacles  opposed  the  progress.  It  appeared  that 
the  men  of  genius  of  the  illustrious  period  had  to  some  extent  practised 
bad  building  and  the  whole  framework  threatened  to  cave  in  unless 
the  passages  were  newly  supported  and  the  oncoming  floods  of  doubt 
conducted  away.  For  two  generations  a  considerable  share  of  the 
efforts  of  mathematics  must  be  applied  to  the  hard  work  of  security 
and  safety,  a  labor  from  which  even  the  greatest  .  .  .  have  not  held 
back. 

NINETEENTH  CENTURY  MATHEMATICS.  —  As  in  the  century 
following  Newton  France  became  the  great  centre  of  mathe- 
matical activity,  so  in  the  nineteenth  century  the  leadership 
passed  to  Germany,  under  the  inspiration  of  Gauss  and  Riemann 
of  Gottingen,  Jacobi  of  Konigsberg,  Weierstrass  of  Berlin, — 
to  mention  but  a  few  of  those  no  longer  living.  Outside  of  Ger- 
many conspicuous  names  are  Cauchy,  Galois,  Hermite,  Legendre, 
and  Poincare  in  France,  Cayley  and  Sylvester  in  England,  Abel  in 
Sweden,  and  Lobatchewski  in  Russia. 

Characteristic  of  this  period  are:  the  development  of  a 
general  theory  of  functions  based  on  unifying  coordinating  prin- 
ciples, compensating  the  powerful  specializing  tendencies,  and  a 
profound  critical  revision  of  the  previously  accepted  axioms, 
leading  for  example  to  the  development  of  a  non-Euclidean 
geometry.  In  the  science  generally  there  is  systematic  devel- 
opment of  instruction  and  research,  notably  in  the  German 
universities;  of  publication,  by  the  establishment  of  mathemati- 
cal journals,  and  the  preparation  of  encyclopedias;  numerous 


TENDENCIES  IN  MATHEMATICAL  SCIENCE         337 

national  societies  are  formed,  and  international  congresses  held. 
These  tendencies  are  naturally  not  confined  to  the  mathemat- 
ical sciences.  In  some  respects  mathematics  has  merely  en- 
joyed its  share  in  the  prosperity  of  a  more  scientific  age,  in  some 
it  has  perhaps  suffered,  at  any  rate  relatively,  from  the  powerful 
stimulus  given  the  natural  sciences  by  the  working  out  of  evolu- 
tionary theories.  From  a  position  of  acknowledged  primacy 
among  a  small  number  of  recognized  sciences,  it  has  come  to  be 
regarded  as  but  one  of  many. 

It  is  impossible  here  even  to  enumerate  the  different  branches 
of  mathematical  science  developed  during  this  period.  Certain 
typical  features  may  however  be  touched  upon. 

NON-EUCLIDEAN  GEOMETRY.  —  Each  century  takes  over  as  a 
heritage  from  its  predecessors  a  number  of  problems  whose  solution 
previous  generations  of  mathematicians  have  arduously  but  vainly 
sought.  It  is  a  signal  achievement  of  the  nineteenth  century  to  have 
triumphed  over  some  of  the  most  celebrated  of  these  problems. 

The  most  ancient  of  them  is  the  quadrature  of  the  circle,  which 
already  appears  in  our  oldest  mathematical  document,  the  Papyrus 
Rhind,  B.C.  2000.  Its  impossibility  was  finally  shown  by  Lindemann, 
1882. 

But  of  all  problems  which  have  come  down  from  the  past,  by  far 
the  most  celebrated  and  important  relates  to  Euclid's  parallel  axiom. 
Its  solution  has  profoundly  affected  our  views  of  space  and  given  rise  to 
questions  even  deeper  and  more  far-reaching,  which  embrace  the  entire 
foundation  of  geometry  and  our  space  conception. —  Pierpont  (1904). 

I  am  convinced  more  and  more  that  the  necessary  truth  of  our 
geometry  cannot  be  demonstrated,  at  least  not  by  the  human  intellect 
to  the  human  understanding.  Perhaps  in  another  world  we  may  gain 
other  insights  into  the  nature  of  space  which  at  present  are  unattain- 
able to  us.  Until  then  we  must  consider  geometry  as  of  equal  rank 
not  with  arithmetic,  which  is  purely  a  priori,  but  with  mechanics. 

—  Gams  (1817). 

There  is  no  doubt  that  it  can  be  rigorously  established  that  the 
sum  of  the  angles  of  a  rectilinear  triangle  cannot  exceed  180°.  But 
it  is  otherwise  with  the  statement  that  the  sum  of  the  angles  cannot 
be  less  than  180° ;  this  is  the  real  Gordian  knot,  the  rocks  which  cause 


338  A  SHORT  HISTORY  OF  SCIENCE 

the  wreck  of  all.  ...  I  have  been  occupied  with  the  problem  over 
thirty  years  and  I  doubt  if  anyone  has  given  it  more  serious  attention, 
though  I  have  never  published  anything  concerning  it. —  Gauss(l824). 
I  will  add  that  I  have  recently  received  from  Hungary  a  little 
paper  on  Non-Euclidean  geometry,  in  which  I  rediscover  all  my  own 
ideas  and  results  worked  out  with  great  elegance.  .  .  .  The  writer 
is  a  very  young  Austrian  officer,  the  son  of  one  of  my  early  friends, 
with  whom  I  often  discussed  the  subject  in  1798,  although  my  ideas 
were  at  that  time  far  removed  from  the  development  and  maturity 
which  they  have  received  through  the  original  reflections  of  this 
young  man.  I  consider  the  young  geometer  von  Bolyai  a  genius  of 
the  first  rank.  —  Gauss  (1832). 

The  gradual  adoption  of  new  and  revolutionary  ideas  on  this 
subject  may  be  further  illustrated  by  the  following  passages :  — 

The  characteristic  features  of  our  space  are  not  necessities  of 
thought,  and  the  truth  of  Euclid's  axioms,  in  so  far  as  they  specially 
differentiate  our  space  from  other  conceivable  spaces,  must  be  es- 
tablished by  experience  and  by  experience  only.  —  R.  S.  Ball. 

If  the  Euclidean  assumptions  are  true,  the  constitution  of  those 
parts  of  space  which  are  at  an  infinite  distance  from  us,  geometry 
upon  the  plane  at  infinity,  is  just  as  well  known  as  the  geometry  of 
any  portion  of  this  room.  In  this  infinite  and  thoroughly  well-known 
space  the  Universe  is  situated  during  at  least  some  portion  of  an 
infinite  and  thoroughly  well-known  time.  So  that  there  we  have 
real  knowledge  of  something  at  least  that  concerns  the  Cosmos; 
something  that  is  true  throughout  the  Immensities  and  the  Eternities. 
That  something  Lobatchewski  and  his  successors  have  taken  away. 
The  geometer  of  today  knows  nothing  about  the  nature  of  the  actually 
existing  space  at  an  infinite  distance;  he  knows  nothing  about  the 
properties  of  this  present  space  in  a  past  or  future  eternity.  He 
knows,  indeed,  that  the  laws  assumed  by  Euclid  are  true  with  an 
accuracy  that  no  direct  experiment  can  approach,  not  only  in  this 
place  where  we  are,  but  in  places  at  a  distance  from  us  that  no  as- 
tronomer has  conceived ;  but  he  knows  this  as  of  Here  and  Now ; 
beyond  this  range  is  a  There  and  Then  of  which  he  knows  nothing  at 
present,  but  may  ultimately  come  to  know  more.  —  Clifford. 

Everything  in  physical  science,  from  the  law  of  gravitation  to 
the  building  of  bridges,  from  the  spectroscope  to  the  art  of  navigation, 


TENDENCIES  IN  MATHEMATICAL  SCIENCE        339 

would  be  profoundly  modified  by  any  considerable  inaccuracy  in  the 
hypothesis  that  our  actual  space  is  Euclidean.  The  observed  truth 
of  physical  science,  therefore,  constitutes  overwhelming  empirical 
evidence  that  this  hypothesis  is  very  approximately  correct,  even 
if  not  rigidly  true.  —  Russell. 

The  most  suggestive  and  notable  achievement  of  the  last  century 
is  the  discovery  of  Non-Euclidean  geometry.  —  Hilbert. 

What  Vesalius  was  to  Galen,  what  Copernicus  was  to  Ptolemy, 
that  was  Lobatchewski  to  Euclid.  There  is,  indeed,  a  somewhat 
instructive  parallel  between  the  last  two  cases.  Copernicus  and 
Lobatchewski  were  both  of  Slavic  origin.  Each  of  them  has  brought 
about  a  revolution  in  scientific  ideas  so  great  that  it  can  only  be  com- 
pared with  that  wrought  by  the  other.  And  the  reason  of  the  trans- 
cendent importance  of  these  two  changes  is  that  they  are  changes 
in  the  conception  of  the  Cosmos.  .  .  .  And  in  virtue  of  these  two 
revolutions  the  idea  of  the  Universe,  the  Macrocosm,  the  All,  as 
subject  of  human  knowledge,  and  therefore  of  human  interest,  has 
fallen  to  pieces.  —  Clifford. 

Geometrical  axioms  are  neither  synthetic  a  priori  conclusions 
nor  experimental  facts.  They  are  conventions :  our  choice,  amongst 
all  possible  conventions,  is  guided  by  experimental  facts;  but  it 
remains  free,  and  is  only  limited  by  the  necessity  of  avoiding  all 
contradiction.  ...  In  other  words,  axioms  of  geometry  are  only 
definitions  in  disguise.  That  being  so  what  ought  one  to  think  of 
this  question :  Is  the  Euclidean  Geometry  true  ?  The  question  is 
nonsense.  One  might  as  well  ask  whether  the  metric  system  is 
true  and  the  old  measures  false ;  whether  Cartesian  co-ordinates  are 
true  and  polar  co-ordinates  false.  —  Poincare. 

To  make  non-Euclidean  geometry  intelligible  to  laymen  the 
following  illustration  has  been  given  by  Helmholtz :  — 

Think  of  the  image  of  the  world  in  a  convex  mirror.  ...  A 
well-made  convex  mirror  of  moderate  aperture  represents  the  objects 
in  front  of  it  as  apparently  solid  and  in  fixed  positions  behind  its 
surface.  But  the  images  of  the  distant  horizon  and  of  the  sun  in  the 
sky  lie  behind  the  mirror  at  a  limited  distance,  equal  to  its  focal 
length.  Between  these  and  the  surface  of  the  mirror  are  found  the 
images  of  all  the  other  objects  before  it,  but  the  images  are  diminished 


340  A  SHORT  HISTORY  OF  SCIENCE 

and  flattened  in  proportion  to  the  distance  of  their  objects  from  the 
mirror.  .  .  .  Yet  every  straight  line  or  plane  in  the  outer  world 
is  represented  by  a  straight  [  ?  ]  line  or  plane  in  the  image.  The  image 
of  a  man  measuring  with  a  rule  a  straight  line  from  the  mirror,  would 
contract  more  and  more  the  farther  he  went,  but  with  his  shrunken 
rule  the  man  in  the  image  would  count  out  exactly  the  same  number 
of  centimeters  as  the  real  man.  And,  in  general,  all  geometrical 
measurements  of  lines  and  angles  made  with  regularly  varying  images 
of  real  instruments  would  yield  exactly  the  same  results  as  in  the 
outer  world,  all  lines  of  sight  in  the  mirror  would  be  represented  by 
straight  lines  of  sight  in  the  mirror.  In  short,  I  do  not  see  how  men 
in  the  mirror  are  to  discover  that  their  bodies  are  not  rigid  solids  and 
their  experiences  good  examples  of  the  correctness  of  Euclidean 
axioms.  But  if  they  could  look  out  upon  our  world  as  we  look  into 
theirs  without  overstepping  the  boundary,  they  must  declare  it  to 
be  a  picture  in  a  spherical  mirror,  and  would  speak  of  us  just  as  we 
speak  of  them;  and  if  two  inhabitants  of  the  different  worlds  could 
communicate  with  one  another,  neither,  as  far  as  I  can  see,  would  be 
able  to  convince  the  other  that  he  had  the  true,  the  other  the  dis- 
torted, relation.  Indeed  I  cannot  see  that  such  a  question  would 
have  any  meaning  at  all,  so  long  as  mechanical  considerations  are 
not  mixed  up  with  it. 

IMAGINARY  NUMBERS.  —  The  solution  of  algebraic  equations 
had  always  been  hampered  by  the  seeming  impossibility  of  per- 
forming the  inverse  processes  involved.  The  equation  x  +  5  =  0 
could  not  be  solved  before  negative  numbers  were  known ;  and  the 
equations  2  x  =  5  and  x2  =  2  would  be  equally  insoluble  without 
fractions  and  irrational  numbers.  Such  equations  as  x2  +  1  =  0 
still  remained  a  stumbling-block  at  the  beginning  of  the  nineteenth 
century.  Gauss  first  pierced  the  mystery  and  released  algebra 
from  its  traditional  restriction,  proving  that  an  equation  of  any 
degree  has  a  corresponding  number  of  roots  of  the  form  a  +  6^  —  1 
—  a  discovery  of  far-reaching  importance  not  merely  for  higher 
mathematics  but  even  for  electrical  engineering. 

That  this  subject  [of  imaginary  magnitudes]  has  hitherto  been 
considered  from  the  wrong  point  of  view  and  surrounded  by  a  mysteri- 
ous obscurity,  is  to  be  attributed  largely  to  an  ill-adapted  notation. 


TENDENCIES  IN  MATHEMATICAL  SCIENCE         341 

If  for  instance,  +  1,  —  1,  V  —  1  had  been  called  direct,  inverse,  and 
lateral  units,  instead  of  positive,  negative,  and  imaginary  (or  even 
impossible)  such  an  obscurity  would  have  been  out  of  the  question. 

—  Gauss. 

Concluding  an  address  on  the  history  of  mathematics  in  the 
nineteenth  century,  a  recent  writer  says :  — 

What  strikes  us  at  once  in  our  survey  of  mathematics  in  the  last 
century  is  its  colossal  proportions  and  rapid  growth  in  nearly  all 
directions,  the  great  variety  of  its  branches,  the  generality  and  com- 
plexity of  its  methods,  an  inexhaustible  creative  imagination,  the  fear- 
less introduction  and  employment  of  ideal  elements,  and  an  apprecia- 
tion for  a  refined  and  logical  development  of  all  its  parts. —  Pierpont. 

Probably  no  other  department  of  knowledge  plays  a  larger  part 
outside  its  own  narrower  domain  than  mathematics.  Some  of  its 
more  elementary  conceptions  and  methods  have  become  part  of  the 
common  heritage  of  our  civilization,  interwoven  in  the  every-day 
life  of  the  people.  Perhaps  the  greatest  labor-saving  invention  that 
the  world  has  seen  belongs  to  the  formal  side  of  mathematics;  I 
allude  to  our  system  of  numerical  notation.  .  .  .  Without  taking 
too  literally  the  celebrated  dictum  of  the  great  philosopher  Kant 
that  the  amount  of  real  science  to  be  found  in  any  special  subject  is 
the  amount  of  mathematics  contained  therein,  it  must  be  admitted 
that  each  branch  of  science  which  is  concerned  with  natural  phe- 
nomena, when  it  has  reached  a  certain  stage  of  development,  becomes 
accessible  to,  and  has  need  of,  mathematical  methods  and  language ; 
this  stage  has,  for  example,  been  reached  in  our  time  by  parts  of  the 
science  of  chemistry.  —  Hobson. 

I  often  say  that  when  you  can  measure  what  you  are  speaking 
about  and  express  it  in  numbers,  you  know  something  about  it ;  but 
when  you  cannot  measure  it,  when  you  cannot  express  it  in  numbers, 
your  knowledge  is  of  a  meager  and  unsatisfactory  kind ;  it  may  be  the 
beginning  of  knowledge,  but  you  have  scarcely  in  your  thoughts 
advanced  to  the  stage  of  science.  —  Kelvin. 

THE  DISCOVERY  OF  NEPTUNE.  —  In  a  century  filled  with  re- 
markable scientific  achievement,  no  single  triumph  has  been  more 
conspicuous,  or  in  some  respects  more  dramatic,  than  the  discovery 
of  the  planet  Neptune  by  Adams  and  Leverrier.  From  the  time 


342  A  SHORT  HISTORY  OF  SCIENCE 

of  Newton  the  perturbations  of  the  planets  had  been  the  subject 
of  continual  observation  and  study.  Improved  telescopes  de- 
manded —  and  at  the  same  time  facilitated  —  more  extended 
and  refined  computations.  Discrepancies  between  computed  and 
observed  positions  indicated  disturbing  forces  of  known  or  in  some 
cases  unknown  origin.  In  particular,  irregularities  —  never  ex- 
ceeding two  minutes  of  arc  —  in  the  motion  of  the  most  recently 
discovered  planet  Uranus,  led  the  young  Cambridge  graduate 
John  Couch  Adams  (1819-1892)  and  the  eminent  French  astrono- 
mer Leverrier  (1811-1877)  to  independent  attacks  on  the  for- 
midable problem  of  determining  the  mass  and  position  of  a 
hypothetical  new  planet  which  could  cause  the  observed  effects 
on  Uranus.  Unfortunately  for  Adams  the  necessary  cooperation 
on  the  part  of  the  observatories  was  not  promptly  available,  so 
that  the  actual  discovery  connected  itself  with  the  somewhat 
later  work  of  Leverrier.  The  discovery  was  naturally  accepted 
as  an  extraordinary  illustration  of  the  power  of  mathematical  as- 
tronomy and  a  convincing  proof  of  the  Newtonian  theory  of 
gravitation. 

The  discovery  of  this  planet  [Neptune]  is  justly  reckoned  as 
the  greatest  triumph  of  mathematical  astronomy.  Uranus  failed 
to  move  precisely  in  the  path  which  the  computers  predicted  for  it, 
and  was  misguided  by  some  unknown  influence  to  an  extent  which 
a  keen  eye  might  almost  see  without  telescopic  aid.  .  .  .  These 
minute  discrepancies  constituted  the  data  which  were  found  sufficient 
for  calculating  the  position  of  a  hitherto  unknown  planet,  and  bring- 
ing it  to  light.  Leverrier  wrote  to  Galle,  in  substance :  Direct  your 
telescope  to  a  point  on  the  ecliptic  in  the  constellation  of  Aquarius,  in 
longitude  826°,  and  you  will  find  within  a  degree  of  that  place  a  new 
planet,  looking  like  a  star  of  about  the  ninth  magnitude,  and  having  a 
perceptible  disc.  The  planet  was  found  at  Berlin  on  the  night  of 
Sept.  26,  1846,  in  exact  accordance  with  this  prediction,  within  half 
an  hour  after  the  astronomers  began  looking  for  it,  and  only  about 
52'  distant  from  the  precise  point  that  Leverrier  had  indicated. 

—  Young. 

While  the  telescope  serves  as  a  means  of  penetrating  space,  and 
of  bringing  its  remotest  regions  nearer  us,  mathematics,  by  inductive 


TENDENCIES  IN  MATHEMATICAL  SCIENCE        343 

reasoning,  has  led  us  onwards  to  the  remotest  regions  of  heaven, 
and  brought  a  portion  of  them  within  the  range  of  our  possibilities ; 
nay,  in  our  own  times  —  so  propitious  to  the  extension  of  knowledge 
—  the  application  of  all  the  elements  yielded  by  the  present  condi- 
tions of  astronomy  has  even  revealed  to  the  intellectual  eyes  a  heavenly 
body,  and  assigned  to  it  its  place,  orbit,  mass,  before  a  single  telescope 
has  been  directed  towards  it.  —  Humboldt. 

COSMIC  EVOLUTION.  —  Reference  has  been  made  to  the  nebular 
hypothesis  included  by  Laplace  in  his  extended  discussion  of  the 
solar  system.  During  the  nineteenth  century  this  theory  has 
been  subjected  to  searching  scrutiny  from  many  points  of  view 
-and  much  doubt  has  been  cast  on  its  validity. 

The  following  summary  of  present  opinion  is  given  by  Hale  in 
his  Stellar  Evolution :  — 

The  nebular  hypothesis  of  Laplace  still  remains  as  the  most  seri- 
ous attempt  to  exhibit  the  development  of  the  solar  system.  At- 
tacked on  many  grounds,  and  showing  signs  of  weakness  that  seem  to 
demand  radical  modification  of  Laplace's  original  ideas,  it  nevertheless 
presents  a  picture  of  the  solar  system  which  has  served  to  connect  in 
a  general  way  a  mass  of  individual  phenomena,  and  to  give  signifi- 
cance to  apparently  isolated  facts  that  offer  little  of  interest  with- 
out the  illumination  of  this  governing  principle. 

We  are  now  in  a  position  to  regard  the  study  of  evolution  as  that 
of  a  single  great  problem,  beginning  with  the  origin  of  the  stars  in 
the  nebulae  and  culminating  in  those  difficult  and  complex  sciences 
that  endeavor  to  account,  not  merely  for  the  phenomena  of  life,  but 
for  the  laws  which  control  a  society  composed  of  human  beings. 

As  a  complement  to  the  preceding  may  be  added  the  following 
from  another  specialist  in  planetary  evolution :  — 

It  is  to  the  glory  of  astronomy  that  in  it  were  initiated  the  two 
most  fundamental  intellectual  movements  in  the  history  of  mankind, 
viz.  the  establishment  of  the  possibility  of  science  and  of  the  doctrine 
of  evolution.  Our  intellectual  ancestors  in  the  valleys  of  the  Euphrates 
and  the  Nile  and  on  the  hills  of  Greece  looked  up  into  the  sky  at 
night  and  saw  order  there  and  not  chaos.  By  painstaking  obser- 


344  A  SHORT  HISTORY  OF  SCIENCE 

vations  and  calculations  they  discovered  the  relatively  simple  laws 
of  the  motions  of  the  heavenly  bodies,  whose  invariable  and  exact 
fulfilment  led  to  the  belief  that  the  whole  universe  in  all  its  parts 
is  orderly  and  that  science  is  possible.  In  the  modern  world  this 
conclusion  is  so  commonplace  that  its  immense  value  is  apt  to  be 
overlooked,  but  a  study  of  the  superstitions  and  the  hopeless  stagna- 
tion of  those  portions  of  mankind  which  have  not  yet  made  the  dis- 
covery gives  us  some  measure  of  its  worth.  The  modern  supplement 
to  the  conception  that  the  universe  is  not  a  chaos  is  that  not  only  is 
it  an  orderly  universe  at  any  instant,  but  that  it  changes  from  one 
state  to  another  in  a  continuous  and  orderly  fashion.  This  doctrine 
that  science  is  extensive  in  time,  as  well  as  in  space,  is  the  funda- 
mental element  in  the  theory  of  evolution  and  the  completion  of  the 
conception  of  science  itself.  The  ideas  of  evolution  in  a  scientific 
form  were  first  applied  to  the  relatively  simple  celestial  phenomena. 
More  than  a  century  before  the  appearance  of  Darwin's  'Origin  of 
Species/  and  the  philosophical  writings  of  Spencer,  another  English- 
man, Thomas  Wright,  published  a  book  on  the  origin  of  worlds.  La- 
place's nebular  hypothesis  gave  the  geologists  a  basis  for  their  work, 
which  in  turn  paved  the  way  for  that  of  Darwin.  For  half  a  century 
now,  the  doctrine  of  evolution  has  been  a  fundamental  factor  in  the 
elaboration  of  all  scientific  theories,  and  its  influence  has  spread  to 
every  field  of  intellectual  effort.  It  has  been  the  good  fortune  of 
mankind  that  his  skies  have  sometimes  been  free  of  clouds  and  that 
he  has  been  able  to  observe  those  relatively  simple  yet  majestic  and 
impersonal  celestial  phenomena  which  have  not  only  led  to  so  im- 
portant results  as  the  founding  of  science  and  the  doctrine  of  evolu- 
tion, but  have  strongly  colored  his  poetry,  philosophy  and  religion, 
and  have  stimulated  him  to  the  elaboration  of  some  of  his  most  pro- 
found mathematical  theories.  —  Moulton. 

DISTANCE  OF  THE  STARS.  —  Among  other  astronomical  dis- 
coveries bearing  a  notable  relation  to  the  history  of  mathematical 
science  is  that  of  measurable  stellar  parallax  by  Bessel  (1784- 
1846).  One  of  the  traditional  objections  to  the  Copernican  theory 
had  been  the  fact  that  no  change  could  be  detected  in  the  relative 
position  of  the  stars,  such  as  would  apparently  result  from  revolu- 
tion of  the  earth  in  a  vast  orbit.  Now  with  more  and  more 
powerful  instruments  it  turned  out  that  there  were  stars  near 


TENDENCIES  IN  MATHEMATICAL  SCIENCE        345 

enough  to  show  precisely  the  displacement  discovered.  In  1837 
Bessel  attacked  this  ancient  problem  successfully  by  making 
extremely  accurate  observation  of  the  relative  positions  of  a  certain 
double  star  (71  Cygni)  and  its  celestial  neighbors.  He  obtained 
for  the  distance  of  the  double  star  657,000  times  the  mean  dis- 
tance from  the  earth  to  the  sun.  Such  inconceivably  vast  dis- 
tances have  been  since  conveniently  expressed  in  a  unit  called  the 
light-year,  i.e.  the  distance  a  ray  of  light  travels  in  an  entire  year 
at  186,000  miles  per  second. 

MATHEMATICAL  PHYSICS.  —  The  further  progress  of  applied 
mathematics  in  the  nineteenth  century  has  been  interestingly 
summarized  by  Woodward  in  a  presidential  address  to  the  Ameri- 
can Mathematical  Society,  from  which  the  following  extracts  are 
quoted. 

Next  came  the  splendid  contributions  of  George  Green  under 
the  modest  title  of  'An  essay  on  the  application  of  mathematical 
analysis  to  the  theories  of  electricity  and  magnetism/  It  is  in  this 
essay  that  the  term  ' potential  function'  first  occurs.  Herein  also 
his  remarkable  theorem  in  pure  mathematics,  since  universally  known 
as  Green's  theorem,  and  probably  the  most  important  instrument 
of  investigation  in  the  whole  range  of  mathematical  physics,  made  its 
appearance.  We  are  all  now  able  to  understand,  in  a  general  way  at 
least,  the  importance  of  Green's  work,  and  the  progress  made  since 
the  publication  of  his  essay  in  1828.  But  to  fully  appreciate  his 
work  and  subsequent  progress  one  needs  to  know  the  outlook  for  the 
mathematico-physical  sciences  as  it  appeared  to  Green  at  this  time 
and  to  realize  his  refined  sensitiveness  in  promulgating  his  discoveries. 
'It  must  certainly  be  regarded  as  a  pleasing  prospect  to  analysts/ 
he  says  in  his  preface, '  that  at  a  time  when  astronomy,  from  the  state 
of  perfection  to  which  it  has  attained,  leaves  little  room  for  further 
applications  of  their  art,  the  rest  of  the  physical  sciences  should  show 
themselves  daily  more  and  more  willing  to  submit  to  it.'  .  .  . '  Should 
the  present  essay  tend  in  any  way  to  facilitate  the  application  of 
analysis  to  one  of  the  most  interesting  of  the  physical  sciences,  the 
author  will  deem  himself  amply  repaid  for  any  labor  he  may  have 
bestowed  upon  it ;  and  it  is  hoped  the  difficulty  of  the  subject  will 
incline  mathematicians  to  read  this  work  with  indulgence,  more  partic- 


346  A   SHORT    HISTORY   OF    SCIENCE 

ularly  when  they  are  informed  that  it  was  written  by  a  young  man  who 
has  been  obliged  to  obtain  the  little  knowledge  he  possesses,  at  such 
intervals  and  by  such  means  as  other  indispensable  avocations  which 
offer  but  few  opportunities  of  mental  improvement,  afforded/  Where 
in  the  history  of  science  have  we  a  finer  instance  of  that  sort  of  modesty 
which  springs  from  a  knowledge  of  things  ? 

Just  as  the  theories  of  astronomy  and  geodesy  originated  in  the 
needs  of  the  surveyor  and  navigator,  so  has  the  theory  of  elasticity 
grown  out  of  the  needs  of  the  architect  and  engineer.  From  such 
prosaic  questions,  in  fact,  as  those  relating  to  the  stiffness  and  the 
strength  of  beams,  has  been  developed  one  of  the  most  comprehensive 
and  most  delightfully  intricate  of  the  mathematico-physical  sciences. 
Although  founded  by  Galileo,  Hooke,  and  Mariotte  in  the  seventeenth 
century,  and  cultivated  by  the  Bernoullis  and  Euler  in  the  last 
century,  it  is,  in  its  generality,  a  peculiar  product  of  the  present 
century.  It  may  be  said  to  be  the  engineers'  contribution  of  the  cen- 
tury to  the  domain  of  mathematical  physics,  since  many  of  its  most 
conspicuous  devotees,  like  Navier,  Lame,  Rankine,  and  Saint-Venant, 
were  distinguished  members  of  the  profession  of  engineering.  .  .  . 

The  theory  of  elasticity  has  for  its  object  the  discovery  of  the 
laws  which  govern  the  elastic  and  plastic  deformation  of  bodies  or 
media.  In  the  attainment  of  this  object  it  is  essential  to  pass  from 
the  finite  and  grossly  sensible  parts  of  media  to  the  infinitesimal  and 
faintly  sensible  parts.  Thus  the  theory  is  sometimes  called  molec- 
ular mechanics,  since  its  range  extends  to  infinitely  small  particles 
of  matter  if  not  to  the  ultimate  molecules  themselves.  It  is  easy, 
therefore,  considering  the  complexity  of  matter  as  we  know  it  in  the 
more  elementary  sciences,  to  understand  why  the  theory  of  elasticity 
should  present  difficulties  of  a  formidable  character  and  require  a 
treatment  and  a  nomenclature  peculiarly  its  own.  .  .  . 

It  is  from  such  elementary  dynamical  and  kinematical  considera- 
tions as  these  that  this  theory  has  grown  to  be  not  only  an  indis- 
pensable aid  to  the  engineer  and  physicist,  but  one  of  the  most  at- 
tractive fields  for  the  pure  mathematician.  As  Pearson  has  remarked, 
'There  is  scarcely  a  branch  of  physical  investigation,  from  the  plan- 
ning of  a  gigantic  bridge  to  the  most  delicate  fringes  of  color  exhibited 
by  a  crystal,  wherein  it  does  not  play  its  part/  It  is,  indeed,  funda- 
mental in  its  relations  to  the  theory  of  structures,  to  the  theory  of 
hydromechanics,  to  the  elastic  solid  theory  of  light,  and  to  the  theory 
of  crystalline  media. 


TENDENCIES  IN  MATHEMATICAL  SCIENCE         347 


REFERENCES  FOR  READING 

CLERKE.     History  of  Astronomy  during  the  Nineteenth  Century. 

CLERKE.     The  Herschels  and  Modern  Astronomy. 

HALE.     Stellar  Evolution. 

LODGE.     Pioneers  of  Science. 

MACH.     Science  of  Mechanics. 

MERZ.     History  of  European  Thought  in  the  Nineteenth  Century,  Chapters 

IV,  V. 

WHITEHEAD.     Introduction  to  Mathematics. 
POINCARE.    Science  and  Hypothesis. 


CHAPTER  XVI 

SOME    ADVANCES    IN    PHYSICAL    SCIENCE    IN    THE 

NINETEENTH   CENTURY.     ENERGY  AND 

THE   CONSERVATION   OF   ENERGY 

About  a  century  after  the  publication  of  the  Principia,  which,  by 
propounding  the  gravitation  formula,  raised  the  ancient  and  indefinite 
notion  of  Attraction  to  the  rank  of  a  useful  and  rigorously  defined 
expression,  another  favorite  theory  [Atomism]  of  the  ancient  philoso- 
phers was  similarly  elevated  to  the  rank  of  a  leading  and  useful 
scientific  idea. 

The  law  of  gravitation  embraced  cosmical  and  some  molar  phe- 
nomena, but  led  to  vagueness  when  applied  to  molecular  actions.  The 
atomic  theory  led  to  a  complete  systematization  of  chemical  com- 
pounds, but  afforded  no  clue  to  the  mysteries  of  chemical  affinity. 
And  the  kinetic  or  mechanical  theories  of  light,  of  electricity  and  mag- 
netism, led  rather  to  a  new  dualism,  the  division  of  science  into  sciences 
of  matter  and  of  the  ether.  ...  A  more  general  term  had  to  be  found 
under  which  the  different  terms  could  be  comprised,  which  would  give 
a  still  higher  generalization,  a  more  complete  unification  of  knowl- 
edge. One  of  the  principal  performances  of  the  second  half  of  the  nine- 
teenth century  has  been  to  find  this  more  general  term,  and  to  trace 
its  all-pervading  existence  on  a  cosmical,  a  molar,  and  a  molecular 
scale  .  .  .  this  greatest  of  all  exact  generalizations  —  the  conception 
of  energy. 

Electrified  and  magnetised  bodies  attract  or  repel  each  other  accord- 
ing to  laws  discovered  by  men  who  never  doubted  that  the  action 
took  place  at  a  distance,  without  the  intervention  of  any  medium, 
and  who  would  have  regarded  the  discovery  of  such  a  medium  as 
complicating  rather  than  as  explaining  the  undoubted  phenomena  of 
attraction.  —  Merz. 

Through  metaphysics  first;  then  through  alchemy  and  chemis- 
try, through  physical  and  astronomical  spectroscopy,  lastly  through 
radio-activity,  science  has  slowly  groped  its  way  to  the  atom. — 
Soddy. 

348 


PHYSICAL  SCIENCE  IN  THE  NINETEENTH  CENTURY     349 

There  is  in  nature  a  certain  magnitude  of  unsubstantial  quality, 
which  keeps  its  value  under  all  alterations  of  the  objects  observed, 
while  its  manner  of  appearance  changes  most  variously.  —  Mayer. 

I  shall  lose  no  time  in  repeating  and  extending  these  experi- 
ments, being  satisfied  that  the  grand  agents  of  nature  are,  by  the 
Creator's  fiat,  indestructible;  and  that  whatever  mechanical  force  is 
expended,  an  exact  equivalent  of  heat  is  always  obtained.  —  Joule. 

Heat  and  work  are  equivalent.  The  entropy  of  the  universe  tends 
to  a  maximum.  —  Claudius. 

The  later  eighteenth  and  the  whole  of  the  nineteenth 
centuries  are  characterized  by  increasingly  rapid  development  of 
the  physical  sciences,  which  become  more  and  more  completely 
differentiated,  and  more  and  more  important  in  their  influence 
upon  industry  and  civilization.  While  it  is  evidently  impossible 
within  our  available  space  to  describe  all  phases  of  this  varied 
development,  we  shall  attempt  to  enumerate  some  of  those  which 
are  most  general  in  their  character  and  most  far-reaching  in  their 
consequences.  A  relatively  complete  and  highly  instructive 
review  of  the  whole  subject  may  be  found  in  Merz's  History 
of  European  Thought  in  the  Nineteenth  Century. 

At  the  beginning  of  this  century  mathematics  was  in  a  stage  of 
triumphant  expansion,  in  which  the  related  sciences  of  astronomy 
and  mechanics  participated.  General  physics  and  chemistry 
were  still  in  the  preliminary  stage  of  collecting  and  coordinating 
data,  with  attempts  at  quantitative  interpretation,  while  in  their 
train  the  natural  sciences  were  following  somewhat  haltingly. 

The  most  notable  advance  in  physical  science  during  the  century 
is  the  gradual  working  out  of  the  great  fundamental  principle  of 
the  conservation  of  energy,  affecting  profoundly  the  whole  range 
of  phenomena.  Of  equal  —  or  even  greater  —  importance  is 
the  gradual  realization  of  progressive  development  —  evolution  — 
not  only  in  plant  and  animal  life  but  even  in  the  inorganic  world. 
Physics  is  gradually  enriched  by  experimental  researches  and 
by  the  working  out  of  mathematical  theories  of  heat,  light, 
magnetism  and  electricity.  Chemistry,  largely  hitherto  a  collec- 
tion of  unrelated  facts,  becomes  more  and  more  coordinated  with 


350  A  SHORT  HISTORY  OF  SCIENCE 

physics  and  mathematics  by  means  of  the  spectroscope,  the 
principle  of  the  conservation  of  energy,  the  atomic  theory,  the 
kinetic  theory  of  gases,  and  the  study  of  molecular  structure. 
On  the  other  hand,  its  relations  with  the  organic  world  are 
made  more  clear  through  the  investigation  of  the  compounds  of 
carbon. 

All  other  sciences,  pure  and  applied,  as  well  as  the  industries, 
profit  unexpectedly  and  almost  inconceivably  by  these  nine- 
teenth century  advances  in  physics  and  chemistry.  The  older 
observational  and  mathematical  astronomy  achieves  a  marvellous 
triumph  in  the  discovery  of  a  new  planet  Neptune,  as  related  in 
Chapter  XV,  and  even  this  is  soon  rivalled  by  the  startling 
achievements  of  the  new  physical  and  chemical  astronomy. 

Reserving  for  the  following  chapter  a  sketch  of  the  develop- 
ment of  the  natural  sciences  under  the  ultimately  dominant  in- 
fluence of  the  theory  of  evolution,  we  proceed  to  outline  briefly 
some  of  the  more  notable  advances  in  the  physical  sciences. 

MODERN  PHYSICS.  —  Some  of  the  main-  features  in  the  develop- 
ment of  physics  in  the  nineteenth  century  have  been  : — the  working 
out  of  consistent  theories  of  light  and  radiant  heat  as  wave  phe- 
nomena of  a  peculiar  hypothetical  medium  called  the  "ether"; 
the  extensive  investigation  of  electrical  and  magnetic  phenomena 
and  the  development  of  an  electromagnetic  theory  even  so  far  as 
to  include  optics ;  the  working  out  of  a  kinetic  theory  of  gases 
with  important  relations  to  chemical  as  well  as  physical  theory; 
the  elaboration  of  general  theories  of  matter,  force,  and  energy, 
all  culminating  in  the  crowning  discovery  of  the  great  unifying 
principle  of  the  Conservation  of  Energy. 

HEAT,  THERMOMETRY  :  CARNOT,  RUMFORD.  —  The  invention 
of  the  thermometer  has  been  traced  in  Chapter  XII.  To  the 
nineteenth  century  belongs  the  determination  of  an  absolute 
scale  1  as  distinguished  from  the  arbitrary  one  previously  employed. 

The  idea  that  heat  is  not  a  substance  but  a  mode  of  molecular 
motion  arose  in  the  seventeenth  and  eighteenth  centuries,  but  was 

1  The  absolute  scale  is  based  on  the  indirect  determination  of  a  temperature 
(—  273°  Centigrade  =  —  459°  Fahrenheit)  at  which  the  internal  activity  which 
constitutes  heat  is  supposed  to  ceaae. 


PHYSICAL  SCIENCE  IN  THE  NINETEENTH  CENTURY     351 

first  given  a  substantial  experimental  basis  by  the  researches  of 
Benjamin  Thompson,  Count  Rumford  (1753-1814),  who  showed 
that  by  friction  of  two  bodies  an  unlimited  amount  of  heat  could  be 
generated.  His  results  were  reported  to  the  Royal  Society  in  1798. 

Rumford  made  a  cylinder  of  gun-metal  rotate  in  a  box  contain- 
ing water,  and  by  the  friction  of  a  revolving  borer  driven  by  horse- 
power  the  water  was  heated  to  boiling  in  two  and  a  half  hours. 

Deeply  impressed  he  exclaims : 

What  is  heat  ?  Is  there  any  such  thing  as  an  igneous  fluid  ?  .  .  . 
Anything  which  any  insulated  body,  or  system  of  bodies,  can  continue 
to  furnish  without  limitation,  cannot  possibly  be  a  material  substance ; 
and  it  appears  to  me  to  be  extremely  difficult,  if  not  quite  impossible, 
to  form  any  distinct  idea  of  anything,  capable  pf  being  excited,  and 
communicated,  in  the  manner  the  heat  was  excited  and  communicated 
in  these  experiments,  except  it  be  MOTION. 

The  "mechanical  equivalent  of  heat" — i.e.  the  work  required 
to  heat  one  pound  of  water  one  degree  —  was  roughly  calculated. 
Epoch-making  in  the  theory  of  heat  were  the  researches  of 
Sadi  Carnot  (1796-1832),  whose  words  follow: 

Wherever  there  is  a  difference  of  temperature  followed  by  return  to 
equilibrium  the  generation  of  power  may  take  place.  Water  vapor  is 
one  means,  but  not  the  only  one.  ...  A  solid  body,  for  example  a 
metal  bar,  gains  and  loses  in  length  when  it  is  alternately  heated  and 
cooled,  and  thus  is  able  to  move  bodies  fastened  to  its  ends.  .  .  . 

The  whole  process  he  pictures  as  a  cycle  in  which  a  certain 
portion  of  the  heat  applied  is  converted  into  work,  a  certain  other 
portion  being  lost.  Thus  the  new  science  of  thermodynamics  was 
born.  The  thorough  and  complete  investigation  of  the  "me- 
chanical equivalent  of  heat"  belongs  to  J.  P.  Joule  (1818-1889) 
of  Manchester,  England,  a  pupil  of  Dalton  the  chemist. 

LIGHT  ;  WAVE  THEORY,  VELOCITY  :  YOUNG,  FRESNEL. —  As 
stated  in  Chapter  XIV  Huygens  had  supported  a  wave  theory  of 
light,  while  Newton  accepted  an  emission  theory.  That  sound 
was  propagated  by  atmospheric  waves  was  well  known.  There  was 
a  troublesome  contrast  however  in  the  phenomenon  of  shadows. 


352  A  SHORT  HISTORY  OF  SCIENCE 

How  could  wave-propagation  be  reconciled  with  sharply  defined 
shadows?  Why  should  not  light  "go  round  a  corner"  as  well  as 
sound  ?  These  difficulties  were  met  by  Thomas  Young  who  re- 
vived Huygens'  wave  theory,  which  was  definitively  established 
by  FresnePs  researches  on  refraction,  beginning  in  1815. 

The  determination  of  the  velocity  of  light  by  observations  of 
the  moons  of  Jupiter  has  been  mentioned  already  (page  286). 
About  1850  this  problem  was  solved  by  a  new  method  devised  by 
Fizeau.  A  ray  of  light  passes  between  the  teeth  of  a  wheel  to  a 
mirror  and  back  again.  During  the  time  required  by  the  ray  to 
pass  thus  out  and  back,  the  gap  through  which  it  has  passed  may 
have  been  just  replaced  by  a  tooth,  in  which  case  the  light  will  be 
intercepted.  By  measuring  the  speed  of  the  wheel  when  varied  in 
a  definite  way  the  speed  of  the  light  ray  may  be  determined.  The 
result  agreed  with  that  obtained  by  the  astronomical  method  within 
about  .5  %.  At  almost  the  same  time  Foucault,  by  an  ingenious 
laboratory  device,  proved  that  light  travels  more  slowly  in  water 
than  in  air  —  a  result  incompatible  with  the  emission  theory. 

The  sporadic  beginnings  of  a  genuine  kinetic  view  of  natural 
phenomena,  after  having  been  cultivated  ...  by  Huygens  and  Euler, 
and  early  in  the  nineteenth  century  by  Rumford  and  Young,  were 
united  into  a  consistent  physical  theory  by  Fresnel,  who  has  been 
termed  the  Newton  of  optics,  and  who  consistently,  and  all  but  com- 
pletely, worked  out  one  great  example  of  this  kind  of  reasoning.  He 
has  the  glory  of  having  not  only  established  the  undulatory  theory  of 
light  on  a  firm  foundation,  but  still  more  of  having  impressed  natural 
philosophers  with  the  importance  of  studying  the  laws  of  regular 
vibratory  motion  and  the  phenomena  of  periodicity  in  the  most  general 
manner. 

In  astronomy  and  optics  the  suggestion  of  common  sense,  which 
regards  the  earth  as  stationary  and  light  as  an  emission  travelling  in 
straight  lines,  had  indeed  allowed  a  certain  amount  of  definite  know- 
ledge ...  to  be  accumulated.  A  real  physical  theory,  however,  was 
impossible  until  the  notions  suggested  by  common  sense  were  com- 
pletely reversed,  and  an  ideal  construction  put  in  the  place  of  a  seem- 
ingly obvious  theory.  This  was  done  in  astronomy  at  one  stroke  by 
Copernicus;  in  optics  only  gradually,  tentatively,  and  hesitatingly. 


PHYSICAL  SCIENCE  IN  THE  NINETEENTH  CENTURY     353 

Newton  himself  had  pronounced  the  pure  emission  theory  to  be 
insufficient  —  and  only  a  preliminary  formulation. 

Young  boldly  generalized  the  undulatory  theory  by  maintaining  that 
"  a  luminif erous  ether  pervades  the  universe,  rare  and  elastic  in  a  high 
degree,"  that  the  sensation  of  different  colors  depends  on  the  different 
frequency  of  vibration  excited  by  light  in  the  retina.  .  .  . 

In  January,  1817,  long  before  Fresnel  had  made  up  his  mind  to  adopt 
a  similar  conclusion  .  .  .  Young  announced  in  a  letter  .  .  .  that  in 
the  assumption  of  transverse  vibrations,  after  the  manner  of  the  vibra- 
tions of  a  stretched  string,  lay  the  possibility  of  explaining  polariza- 
tion. ...  —  Merz. 

THE  SPECTROSCOPE  AND  SPECTRUM  ANALYSIS.  —  For  closer 
study  of  the  spectrum  of  Newton  and  the  "dark  lines"  observed  by 
Fraunhofer  in  1815  (and  in  1802  by  Wollaston)  in  the  spectrum, 
Kirchhoff  and  Bunsen  in  1859-60  perfected  the  "spectroscope." 
This  is  essentially  no  more  than  a  telescope  so  attached  to  the 
prism  producing  the  spectrum  from  a  slit  as  to  facilitate  minute 
scrutiny  of  the  latter.  It  was  by  these  workers  and  at  this  time 
that  spectrum  analysis  became  firmly  established  as  a  means  of 
detecting  the  chemical  constituents  of  celestial  bodies.  Kirch- 
hoff wrote  in  1859 :  — 

I  conclude  that  colored  flames  in  the  spectra  of  which  bright  lines 
present  themselves,  so  weaken  the  rays  of  the  color  of  these  lines, 
when  such  rays  pour  through  them,  that  in  place  of  the  bright  lines, 
dark  ones  appear  as  soon  as  there  is  brought  behind  the  flame  a  source 
of  light  of  sufficient  intensity  in  which  these  lines  are  otherwise  want- 
ing, thus  originating  two  great  applications  of  his  principle  —  the 
search,  through  the  study  of  the  spectra  of  distant  stellar  sources  of 
light,  after  the  ingredients  which  are  present  in  those  distant  lumi- 
naries, and  the  search,  through  the  study  of  the  flames  of  terrestrial 
substances,  for  new  spectral  lines  announcing  yet  undiscovered  ele- 
ments. 

In  1862,  only  three  years  after  Kirchhoff  and  Bunsen's  application  of 
the  spectroscope  to  the  study  of  the  sun,  Huggins  measured  the  posi- 
tion of  the  lines  in  the  spectra  of  about  forty  stars,  with  a  small  slit 
spectroscope  attached  to  an  8-inch  telescope.  In  1876  he  successfully 
applied  photography  to  a  study  of  the  ultra-violet  region  of  stellar 

2A 


354  A  SHORT  HISTORY  OF  SCIENCE 

spectra,  and  in  1879  published  his  paper  On  the  Photographic  Spectra 
of  Stars.  The  results  were  arranged  and  discussed  with  reference 
to  their  bearing  on  stellar  evolution.  —  Hale. 

The  first  application  of  the  spectroscope  to  the  corona  of  the 
sun  was  made  in  1868  by  Janssen  and  Lockyer,  independently,  re- 
vealing the  chemical  composition  of  the  solar  prominences  as 
chiefly  hydrogen,  calcium,  and  helium. 

ELECTRICITY  AND  MAGNETISM:  FARADAY,  GREEN,  AMPERE, 
MAXWELL. — Seebeck  (1770-1831)  in  his  work  On  the  Magnetism 
of  the  Galvanic  Circuit  published  a  first  account  of  the  magnetic 
field  illustrated  by  magnetized  iron  filings  and  later  so  fruitfully 
investigated  by  Faraday.  The  sciences  of  electricity  and  mag- 
netism had  originated  in  the  latter  part  of  the  eighteenth  century 
with  Coulomb's  use  of  the  torsion-balance,  by  means  of  which  he 
made  accurate  comparison  between  the  attractive  or  repulsive 
forces  exercised  by  electrified  and  magnetized  bodies,  and  the 
mechanical  forces  required  to  twist  wires.  Thus  he  found  the  first 
definite  units,  a  process  carried  much  farther  by  Gauss  and  Weber* 

Ampere  (1775-1836)  stimulated  by  Oersted's  discovery  of  the 
effect  of  the  electric  current  on  magnets,  published  in  1820  a 
fundamental  discussion  of  electrodynamics  and  soon  after  enun- 
ciated his  celebrated  law :  — 

Two  parallel  and  like  directed  currents  attract  each  other,  while 
two  parallel  currents  of  opposite  directions  repel  each  other. 

He  also  succeeded  in  expressing  the  quantitative  relations  in- 
volved by  a  mathematical  formula. 

Faraday,  one  of  the  most  distinguished  investigators  in  the 
whole  history  of  physical  science,  rescued  electricity  from  the 
mysterious  notion  of  currents  acting  on  each  other  through  empty 
space,  by  the  fruitful  conception  of  a  magnetic  field,  of  which  a 
new  and  comprehensive  mathematical  theory  was  gradually  worked 
out  by  Maxwell.  Faraday's  discoveries  were  so  far-reaching  that 
they  have  even  been  coupled  with  the  law  of  the  conservation  of 
energy  and  Darwin's  theory  of  descent  as  the  greatest  scientific 
ideas  of  the  latter  half  of  the  century.  He  observes :  — 


PHYSICAL  SCIENCE  IN  THE  NINETEENTH  CENTURY     355 

Atoms  and  lines  of  force  have  become  a  practical  —  shall  I  say  a 
popular  ?  —  reality,  whereas  they  were  once  only  the  convenient 
method  of  a  single  original  mind  for  gathering  together  and  unifying  in 
thought  a  bewildering  mass  of  observed  phenomena,  or  at  most  capable 
of  being  utilized  for  a  mathematical  description  and  calculation  of 
actual  effects. 

Yet  Helmholtz  says  of  Faraday : 

It  is  indeed  remarkable  in  the  highest  degree  to  observe  how,  by  a 
kind  of  intuition,  without  using  a  single  formula,  he  found  out  a 
number  of  comprehensive  theorems,  which  can  only  be  strictly  proved 
by  the  highest  powers  of  mathematical  analysis.  ...  I  know  how 
often  I  found  myself  despairingly  staring  at  his  descriptions  of  lines  of 
force,  their  number  and  tension,  or  looking  for  the  meaning  of  sen- 
tences in  which  the  galvanic  current  is  defined  as  an  axis  of  force.  .  .  . 

Faraday  apprehended  the  principle  of  the  conservation  of 
energy  even  before  it  had  come  to  clear  expression  as  common 
property,  saying,  for  example,  in  refuting  the  theory  that  elec- 
tricity could  be  generated  by  metallic  contact  alone :  — 

But  in  no  case,  not  even  in  those  of  [electric  fishes],  is  there  a 
pure  creation  or  a  production  of  power  without  a  corresponding  ex- 
haustion of  something  to  supply  it. 

Like  Young,  Dalton,  and  Joule,  Faraday  did  not  belong  to  the 
orthodox  Cambridge  school  then  dominant  in  English  mathe- 
matical and  physical  science,  and  recognition  of  the  significance 
of  his  ideas  was  consequently  retarded. 

What  the  atomic  theory  has  done  for  chemistry,  Faraday's  lines  of 
force  are  now  doing  for  electrical  and  magnetic  phenomena.  .  .  .  Yet 
the  circumstances  under  which  Faraday's  work  was  done  were  those 
of  penury. 

ELECTROMAGNETIC  THEORY  OF  LIGHT. — In  1845  Faraday  writes : 

I  ....  have  at  last  succeeded  in  magnetising  and  electrifying  a 
ray  of  light,  and  in  illuminating  a  magnetic  line  of  force.  .  .  .  Em- 
ploying a  ray  of  light,  we  can  tell,  by  the  eye,  the  direction  of  the 
magnetic  lines  through  a  body :  and  by  the  alteration  of  the  ray  and 
its  optical  effect  on  the  eye,  can  see  the  course  of  the  lines  just  as 
we  can  see  the  course  of  a  thread  of  glass. 


356  A  SHORT  HISTORY  OF  SCIENCE 

I  have  deduced  the  relation  between  the  statical  and  dynamical 
measures  of  electricity,  and  have  shown  by  a  comparison  of  the 
electro-magnetic  experiments  of  Kohlrausch  and  Weber  with  the  veloc- 
ity of  light  as  found  by  Fizeau,  that  the  elasticity  of  the  magnetic 
medium  in  air  is  the  same  as  that  of  the  luminiferous  medium,  if  these 
two  coexistent,  coextensive  and  equally  elastic  media  are  not  rather 
one  medium.  .  .  .  We  can  scarcely  avoid  the  inference  that  light 
consists  in  the  transverse  undulations  of  the  same  medium  which  is 
the  cause  of  electric  and  magnetic  phenomena.  —  Maxwell. 

We  must  not  listen  to  any  suggestion  that  we  may  look  upon  the 
luminiferous  ether  as  an  ideal  way  of  putting  the  thing.  A  real  matter 
between  us  and  the  remoter  stars  I  believe  there  is,  and  that  light 
consists  of  real  motions  of  that  matter,  motions  just  such  as  are 
described  by  Fresnel  and  Young,  motions  in  the  way  of  transverse 
vibrations. 

—  Kelvin,  Baltimore  lecture. 

Hertz,  a  pupil  of  Helmholtz,  first  proved  in  1887  the  existence 
of  those  undulations  which  now  bear  his  name,  showing  also 
that  these  travel  with  the  rapidity  of  light,  and  that  they  are, 
like  light  and  heat  waves,  susceptible  of  reflection,  refraction, 
and  polarization,  and  until  he  measured  their  length  and  velocity, 
no  great  progress  was  made  in  verifying  those  relations  experi- 
mentally. Such  more  recent  applications  of  Hertz's  ideas  as 
radio-telegraphy  and  radio-telephony  testify  to  their  immense 
practical  as  well  as  theoretical  importance. 

With  the  establishment  of  the  electromagnetic  theory  of  light, 
what  we  may  call  the  undulatory  series  became  complete.  Sound 
had  long  been  known  to  be  due  to  waves  or  "undulations  "  and 
the  wave  theory  of  heat  and  of  light  was  accepted,  so  that  it  had 
only  remained  to  prove  the  existence  of  electrical  and  magnetic 
undulations,  and  to  show  that  such  waves  moved  with  the 
velocity  and  other  characteristics  of  light.  This  it  was  which 
was  done  mathematically  by  Maxwell  and  experimentally  by  Hertz. 

The  velocity  of  propagation  of  an  electro-magnetic  disturbance 
in  air  ...  does  not  differ  more  from  the  velocity  of  light  in  air  .  . 
than  the  several  calculated  values  of  these  quantities  differ  among 
each  other.  —  Maxwell. 


PHYSICAL  SCIENCE  IN  THE  NINETEENTH  CENTURY     357 

KINETIC  THEORY  OF  GASES.  CLAUSIUS.  The  modern  theory  of 
gases  was  born  .  .  .  when  Joule  in  1857  actually  calculated  the 
velocity  with  which  a  particle  of  hydrogen  .  .  .  must  be  moving, 
assuming  that  the  atmospheric  pressure  is  equilibrated  by  the 
rectilinear  motion  and  impact  of  the  supposed  particles  of  the  gas  on 
each  other  and  the  walls  of  the  containing  vessel.  This  meant  taking 
the  atomic  view  of  matter  in  real  earnest,  not  merely  symbolically, 
as  chemists  had  done. — Merz. 

The  theory  owes  its  full  development,  however,  to  the  re- 
searches of  Maxwell,  Clausius  and  Boltzmann. 

The  great  turning-point,  indeed,  lay  in  the  kinetic  theory  of  gases, 
which  .  .  .  had  introduced  quite  novel  considerations  by  showing 
how  the  dead  pressure  of  gases  and  vapors  could  be  explained  on  the 
hypothesis  of  a  very  rapid  but  disorderly  translational  movement 
of  the  smallest  particles  in  every  possible  direction. 

THE  CONCEPTION  OP  ENERGY.  —  Newton's  Principia  contains 
by  implication  the  modern  notion  of  energy  —  but  the  first 
clear  and  consistent  fixing  of  the  modern  terminology  is  found 
in  Poncelet's  Mecanique  industrielle,  1829.  The  idea  of  work  was 
thus  developed  from  the  standpoint  of  the  engineer  —  notably 
under  the  influence  of  Rankine ;  while  on  the  other  hand,  it  is  a 
not  less  remarkable  fact  that  Black,  Young,  Mayer  and  Helmholtz 
all  came  to  their  scientific  work  through  another  form  of  applied 
science  —  medicine. 

A  considerable  step  toward  the  general  idea  of  the  conservation 
of  energy  was  taken  by  Rumford  in  his  determination  of  the 
mechanical  equivalent  of  heat,  but  the  final  achievement  is  due 
mainly  to  Joule  in  England  and  Mayer  and  Helmholtz  in  Germany. 
In  1847  Helmholtz  read  before  the  Physical  Society  of  Berlin  one 
of  the  most  remarkable  papers  of  the  century  (Die  Erhaltung 
der  Kraft),  in  which  he  says  with  full  justice:  — 

I  think  in  the  foregoing  I  have  proved  that  the  above  mentioned 
law  does  not  go  against  any  hitherto  known  facts  of  natural  science, 
but  is  supported  by  a  large  number  of  them  in  a  striking  manner.  I 
have  tried  to  enumerate  as  completely  as  possible  what  consequences 
result  from  the  combination  of  other  known  laws  of  nature,  and  how 


358  A  SHORT  HISTORY  OF  SCIENCE 

they  require  to  be  confirmed  by  further  experiments.  The  aim  of  this 
investigation,  and  what  must  excuse  me  likewise  for  its  hypothetical 
sections,  was  to  explain  to  natural  philosophers  the  theoretical  and 
practical  importance  of  the  law,  the  complete  verification  of  which 
may  well  be  looked  upon  as  one  of  the  main  problems  of  physical 
science  in  the  near  future. 

Fifteen  years  later  Helmholtz  spoke  of  the  principle  as  follows :  — 
*  The  last  decades  of  scientific  development  have  led  us  to  the  recogni- 
tion of  a  new  universal  law  of  all  natural  phenomena,  which,  from  its 
extraordinarily  extended  range,  and  from  the  connection  which  it 
constitutes  between  natural  phenomena  of  all  kinds,  even  of  the 
remotest  times  and  the  most  distant  places,  is  especially  fitted  to  give 
us  an  idea  of  what  I  have  described  as  the  character  of  the  natural 
sciences,  which  I  have  chosen  as  the  subject  of  this  lecture.  This  law 
is  the  Law  of  the  Conservation  of  Force,  a  term  the  meaning  of  which 
I  must  first  explain.  It  is  not  absolutely  new ;  for  individual  domains 
of  natural  phenomena  it  was  enunciated  by  Newton  and  Daniel 
Bernoulli;  and  Rumford  and  Humphry  Davy  have  recognised  dis- 
tinct features  of  its  presence  in  the  laws  of  heat.  The  possibility 
that  it  was  of  universal  application  was  first  stated  by  Mayer  in  1842, 
while  almost  simultaneously  with,  and  independently  of  him,  Joule 
made  a  series  of  important  and  difficult  experiments  on  the  relation 
of  heat  to  mechanical  force,  which  supplied  the  chief  points  in  which 
the  comparison  of  the  new  theory  with  experience  was  still  wanting. 
The  law  in  question  asserts,  that  the  quantity  of  force  which  can  be 
brought  into  action  in  the  whole  of  Nature  is  unchangeable,  and  can  neither 
be  increased  nor  diminished. 

This  doctrine  is  now  so  fundamental  and  so  familiar  as  to  require 
no  further  comment.  The  indestructibility  of  matter  had  already 
become  axiomatic.  Henceforth,  energy  also  was  to  be  considered 
constant  and  indestructible. 

DISSIPATION  OF  ENERGY.  —  It  remained  for  William  Thomson 
(Lord  Kelvin),  applying  the  principle  of  the  conservation  of  energy 
to  the  thermodynamic  laws  of  Carnot,  to  deduce  the  other  great 
principle  of  the  Dissipation  of  Energy,  which  recognizes  that 
while  total  energy  is  constant,  useful  energy  is  diminishing  by  the 
continual  degeneration  of  other  forms  into  non-useful  or  dis- 


PHYSICAL  SCIENCE  IN  THE  NINETEENTH  CENTURY     359 

sipated  heat.  All  workers  in  this  field,  from  Carnot  to  Thom- 
son, had  appreciated  the  impossibility  of  "perpetual  motion." 
Helmholtz  expresses  his  appreciation  of  Thomson's  contri- 
bution to  the  theory  in  a  striking  passage : 

We  must  admire  the  acumen  of  Thomson,  who  could  read  between 
the  letters  of  a  mathematical  equation,  for  some  time  known,  which 
spoke  only  of  heat,  volume  and  pressure  of  bodies,  conclusions  which  . 
threaten  the  universe,  though  indeed  only  in  infinite  time,  with  eternal 
death. 

Thomson,  more  than  any  other  thinker,  put  the  problem  into 
common-sense  language.  ...  He  saw  at  once,  when  adopting  Joule's 
doctrine  of  the  convertibility  of  heat  and  mechanical  work,  that,  if 
all  processes  in  the  world  be  reduced  to  those  of  a  perfect  mechanism, 
they  will  have  this  property  of  a  perfect  machine,  namely,  that  it 
can  work  backward  as  well  as  forward.  It  is  against  all  reason  and 
common  sense  to  carry  out  this  idea  in  its  integrity  and  completeness. 
If  then,  the  motion  of  every  particle  of  matter  in  the  universe  were 
precisely  reversed  at  any  instant,  the  course  of  nature  would  be  simply 
reversed  forever  after.  The  bursting  bubble  of  foam  at  the  foot  of  a 
waterfall  would  reunite  and  descend  into  the  water;  the  thermal 
motions  would  reconcentrate  their  energy  and  throw  the  mass  up  the 
fall  in  drops,  re-forming  into  a  close  column  of  ascending  water.  Heat 
which  had  been  generated  by  the  friction  of  solids  and  dissipated  by 
conduction  and  radiation  with  absorption,  would  come  again  to  the 
place  of  contact  and  throw  the  moving  body  back  against  the  force 
to  which  it  had  previously  yielded.  Boulders  would  recover  from  the 
mud  the  materials  required  to  rebuild  them  into  their  previous  jagged 
forms,  and  would  become  re-united  to  the  mountain-peak  from  which 
they  had  formerly  broken  away.  And  also,  if  the  materialistic  hypoth- 
esis of  life  were  true,  living  creatures  would  grow  backwards  with 
conscious  knowledge  of  the  future,  but  with  no  memory  of  the  past, 
and  would  become  again  unborn.  But  the  real  phenomena  of  life 
infinitely  transcend  human  science;  and  speculation  regarding  con- 
sequences of  their  imagined  reversal  is  utterly  unprofitable.  Far 
otherwise,  however,  is  it  in  respect  to  the  reversal  of  the  motions 
of  matter  uninfluenced  by  life,  a  very  elementary  consideration  of 
which  leads  to  the  full  explanation  of  the  theory  of  dissipation  of 
energy. 


360  A  SHORT  HISTORY  OF  SCIENCE 

MODERN  CHEMISTRY.  —  Main  features  in  nineteenth  century 
chemistry  are  :  —  the  discovery  of  the  fundamental  quantitative 
relations  of  chemical  reactions ;  the  development  of  a  consistent 
and  definite  theory  of  atoms,  molecules  and  valence;  the 
synthesis  of  organic  substances;  the  discovery  of  periodic 
relations  and  characteristics ;  the  development  of  ideas  of  chemical 
structure ;  the  development  of  electro-chemistry ;  the  foundation 
of  physical  chemistry. 

With  Lavoisier,  "the  father  of  modern  chemistry,"  the  science, 
heretofore  descriptive  and  empirical,  had  become  quantitative 
and  productive,  seeking  like  the  older  sciences  of  astronomy  and 
physics  to  make  itself  mathematical  —  an  exact  science.  Postu- 
lating the  existence  of  indestructible  elementary  substances, 
Lavoisier  controlled  and  interpreted  chemical  reactions  by  careful 
weighing.  Until  he  entered  the  field  there  was  no  generalization 
wide  enough  to  entitle  chemistry  to  be  called  a  science. 

CHEMICAL  LABORATORIES  :  LIEBIG.  —  In  the  nineteenth 
century  chemical  studies  received  a  powerful  impetus  through  the 
establishment  of  teaching  laboratories  at  the  universities  —  in 
which  Liebig  at  Giessen  in  1826  was  a  pioneer.  He  writes : 

At  Giessen  all  were  concentrated  in  the  work,  and  this  was  a  passion- 
ate enjoyment.  .  .  .  The  necessity  of  an  institute  where  the  pupil 
could  instruct  himself  in  the  chemical  art,  .  .  .  was  then  in  the  air, 
and  so  it  came  about  that  on  the  opening  of  my  laboratory  .  .  .  pupils 
came  to  me  from  all  sides.  ...  I  saw  very  soon  that  all  progress  in 
organic  chemistry  depended  on  its  simplification.  .  .  .  The  first 
years  of  my  residence  at  Giessen  were  almost  exclusively  devoted  to 
the  improvement  of  organic  analysis,  and  with  the  first  successes 
there  began  at  the  small  university  an  activity  such  as  the  world  had 
not  yet  seen.  ...  A  kindly  fate  had  brought  together  in  Giessen  the 
most  talented  youths  from  all  countries  of  Europe.  .  .  .  Every  one 
was  obliged  to  find  his  own  way  for  himself.  .  .  .  We  worked  from 
dawn  to  the  fall  of  night. 

To  investigate  the  essence  of  a  natural  phenomenon,  three 
conditions  are  necessary.  We  must  first  study  and  know  the 
phenomenon  itself,  from  all  sides ;  we  must  then  determine  in  what 
relation  it  stands  to  other  natural  phenomena ;  and  lastly,  when  we 


PHYSICAL  SCIENCE  IN  THE  NINETEENTH  CENTURY     361 

have  ascertained  all  these  relations,  we  have  to  solve  the  problem  of 
measuring  these  relations  and  the  laws  of  mutual  dependence  —  that 
is,  of  expressing  them  in  numbers.  In  the  first  period  of  chemistry, 
all  the  powers  of  men's  minds  were  devoted  to  acquiring  a  knowledge 
of  the  properties  of  bodies.  .  .  .  This  is  the  alchemistical  period. 
The  second  period  embraces  the  determination  of  the  mutual  relations 
or  connections  of  these  properties ;  this  is  the  period  of  phlogistic 
chemistry.  In  the  third  ...  we  ascertain  by  weight  and  measure 
and  express  in  numbers  the  degree  in  which  the  properties  of  bodies 
are  mutually  dependent.  The  inductive  sciences  begin  with  the 
substance  itself,  then  come  just  ideas,  and  lastly,  mathematics  are 
called  in,  and,  with  the  aid  of  numbers,  complete  the  work. 

QUANTITATIVE  RELATIONS  :  ATOMS  ;  MOLECULES  ;  VALENCE.  — 
It  took  .  .  .  nearly  a  century  .  .  .  before  the  rule  of  definite  pro- 
portions was  generally  established,  becoming  a  guide  for  chemical 
analysis.  .  .  . 

The  vaguer  terms  of  chemical  affinity  and  elective  attraction,  of 
chemical  action,  of  adhesion  and  elasticity  .  .  .  gradually  dis- 
appeared, when  by  the  aid  of  the  chemical  balance  each  simple  sub- 
stance and  each  definite  compound  began  to  be  characterized  and 
labelled  with  a  fixed  number.  —  Merz. 

Proust,  analyzing  various  metallic  oxides  and  sulphides,  obtained 
constant  percentage  results,  from  which  however  no  obvious  infer- 
ences could  be  drawn  by  him.  Dalton  (1766-1844)  had  the  happy 
inspiration  to  interpret  these  figures  in  relation  to  weights  of  the 
combined  oxygen,  making  the  lightest  element,  hydrogen,  the  unit  or 
measure  of  his  system.  His  hypothesis  that  elements  combine  in 
weights  proportional  to  small  whole  numbers  —  the  "  law  of  mul- 
tiple proportions,"  has  since  been  verified  by  innumerable  analyses. 

It  has  recently  been  shown  that  Dalton  was  in  the  habit  of 
regarding  all  physical  phenomena  as  the  result  of  the  interaction 
of  small  particles.  He  was  thus  naturally  led  to  the  conception 
of  definite  atomic  weights  to  be  determined  by  experiment.  In 
the  words  of  Dalton  : 

We  can  as  well  undertake  to  incorporate  a  new  planet  in  the  solar 
system  or  to  annihilate  one  there  as  to  create  or  destroy  an  atom  of 


362  A  SHORT  HISTORY  OF  SCIENCE 

hydrogen.  All  the  changes  we  can  effect  consist  in  the  separation  of 
atoms  bound  together  before  and  in  the  union  of  those  previously 
separated. 

The  atomic  theory  while  highly  serviceable  has  always  been 
subjected  to  severe  criticism.  In  1840,  for  example,  Dumas 
declared  that  it  did  not  deserve  the  confidence  placed  in  it,  and  that 
if  he  could  he  would  banish  the  word  "  atom,"  convinced  that 
science  should  confine  itself  to  what  could  be  known  by  experience. 
As  late  as  1852  Frankland  says : 

I  had  not  proceeded  far,  in  the  investigation  of  the  organo-metallic 
compounds  before  the  facts  brought  to  light  began  to  impress  upon  me 
the  existence  of  a  fixity  in  the  maximum  combining  value  or  capacity 
of  saturation  in  the  metallic  elements  which  had  not  before  been  sus- 
pected. ...  It  was  evident  that  the  atoms  of  zinc,  tin,  arsenic  .  .  . 
had  only  room,  ...  for  the  attachment  of  a  fixed  and  definite  number 
of  the  atoms  of  other  elements. 

Independent  researches  have,  in  combination  with  the  older  chemi- 
cal theories,  introduced  so  much  definiteness  into  this  line  of  thought 
that '  the  Newtonian  theory  of  gravitation  is  not  surer  to  us  now  than 
is  the  atomic  or  molecular  theory  in  chemistry  and  physics  —  so  far, 
at  all  events,  as  its  assertion  of  heterogeneousness  in  the  minute 
structure  of  matter,  apparently  homogeneous  to  our  senses,  and  to  our 
most  delicate  direct  instrumental  tests/ — Kelvin,  1886. 

The  three  main  criticisms  of -the  atomic  theory  are:  — 
(1)  that  it  is  based  on  inference,  not  on  direct  observation; 
and  is  therefore  only  a  provisional  hypothesis ;    (2)  that  it  takes 
no    account  of  chemical  forces  —  "affinity";    (3)  that  it  over- 
emphasizes analysis. 

The  idea  of  "atomicity"  and  "valency"  .  .  .  was  not  possible 
without  the  clear  notion  of  the  "molecule"  as  distinct  from  the 
"atom."  This  idea  had  lain  dormant  in  the  now  celebrated  but 
long  forgotten  law  of  Avogadro,  which  was  established  in  1811 
almost  immediately  after  the  appearance  of  Dalton's  atomic  theory. 

It  had  been  known  since  .  .  .  Boyle  and  Mariotte  that  equal 
volumes  of  different  gases  under  equal  pressure  change  their  volumes 
equally  if  the  pressure  is  varied  equally,  and  it  was  also  known  .  .  . 


PHYSICAL  SCIENCE  IN  THE  NINETEENTH  CENTURY     363 

that  equal  volumes  of  different  gases  under  equal  pressure  change  their 
volumes  equally  with  equal  rise  of  temperature.  These  facts  sug- 
gested to  Avogadro,  and  almost  simultaneously  to  Ampere,  the  very 
simple  assumption  that  this  is  owing  to  the  fact  that  equal  volumes  of 
different  gases  contain  an  equal  number  of  the  smallest  independent 
particles  of  matter.  This  is  Avogadro's  celebrated  hypothesis.  It 
was  the  first  step  in  the  direct  physical  verification  of  the  atomic  view 
of  matter.  —  Merz. 

SYNTHESIS  OF  ORGANIC  SUBSTANCES.  —  Until  the  middle  of  the 
nineteenth  century  there  was  an  apparently  fundamental  separa- 
tion between  organic  and  inorganic  nature.  Since  then  they  have 
been  brought  together  by  the  general  laws  of  energy  and  to  some 
extent  by  the  principles  of  evolution,  as  will  appear  in  the  following 
chapter.  In  1828  Wohler  (of  Gottingen)  had  indeed  succeeded 
in  preparing  urea  out  of  inorganic  materials,  a  discovery  which 
disproved  such  difference  as  was  hitherto  considered  to  exist 
between  organic  and  inorganic  bodies. 

A  PERIODIC  LAW  AMONG  THE  ELEMENTS.  —  With  gradually  in- 
creasing knowledge  of  the  fundamental  constants  of  chemistry 
—  the  atomic  weights  —  attempts  were  naturally  made  to  connect 
these  with  the  chemical  and  physical  properties  of  the  correspond- 
ing elements :  valence,  affinity,  specific  gravity,  specific  heat,  etc. 
In  1869-71  Mendelejeff,  a  Russian  chemist,  succeeded  in  establish- 
ing remarkable  relations  between  these  data,  and  on  tabulating 
them  enunciated  his  Periodic  Law,  which  has  resulted  in  the  dis- 
covery of  several  new  and  hitherto  unsuspected  elements.  As  the 
existence  of  the  planet  Neptune  (page  341)  had  been  predicted  to 
fill  an  apparent  gap  in  a  system,  so  Mendelejeff  under  the  periodic 
law  was  able  to  predict  the  existence  of  other  and  missing  ele- 
ments in  the  series  of  chemical  elements.  And  just  as  the  pre- 
diction of  Adams  and  Leverrier  was  fulfilled  by  the  actual  discovery 
of  Neptune,  so  the  prophecy  of  Mendelejeff  was  justified  by  the 
discovery  of  gallium  in  1871,  scandium  in  1879,  and  germanium 
in  1886.  Furthermore,  the  periodic  law  enabled  Mendelejeff 
to  question  the  correctness  of  certain  accepted  atomic  weights,  and 
here,  also,  he  was  justified  by  subsequent  redeterminations. 


364  A  SHORT  HISTORY  OF  SCIENCE 

It  may  be  questioned  whether  the  celebrated  periodic  law  of  New- 
lands,  Lothar  Meyer  and  Mendelejeff,  which  has  brought  some  order 
into  the  atomic  and  other  numbers  referring  to  the  different  elements, 
and  has  even  made  it  possible  to  predict  the  existence  of  unknown  ele- 
ments with  definite  properties,  stands  really  in  a  firmer  position  than 
the  once  well-known  but  now  forgotten  law  of  Bode,  according  to 
which  the  gap  in  the  series  which  gives  the  distances  of  the  planets 
from  the  sun  indicated  the  existence  of  a  planet  between  Mars  and 
Jupiter. 

CHEMICAL  STRUCTURE.  —  Crystallography  —  a  science  of  the 
nineteenth  century  —  established  an  important  connection  be- 
tween chemistry  and  geometry.  Haiiy  made  mineralogy  "as 
precise  and  methodical  as  astronomy.  .  .  .  He  was  to  Werner  and 
Rome  de  Plsle,  his  predecessors,  what  Newton  had  been  to  Kepler 
and  Copernicus." 

In  the  early  years  of  the  atomic  theory  Wollaston  had  predicted 
that  philosophers  would  seek  a  geometrical  conception  of  the 
distribution  of  the  elementary  particles  in  space  —  a  prophecy 
first  practically  fulfilled  by  Van't  Hoff  s  Chemistry  in  Space  (1875). 

The  chemical  character  is  dependent  primarily  upon  the  arrange- 
ment and  number  of  the  atoms,  and  in  a  lesser  degree  upon  their 
chemical  nature  (V.  Meyer) .  The  atomic  view  first  became  a  scientific 
instrument,  when  arithmetical  relations  of  a  definite  and  unalterable 
kind  were  proved  to  exist ;  it  became  a  yet  more  useful  instrument, 
when  to  the  arithmetical  there  were  added  geometrical  conceptions. 

—  Merz. 

PHYSICAL  CHEMISTRY:  ELECTROLYTIC  AND  THERMODYNAMIC 
DEVELOPMENTS  OF  CHEMISTRY.  —  In  the  latter  part  of  the  nine- 
teenth century  much  light  was  thrown  on  a  wide  range  of  physical 
and  chemical  phenomena  by  the  study  of  solutions  and  their 
electrolytic  behavior.  Much  had  already  been  accomplished  by 
Davy  in  the  decomposition  of  substances  by  the  electric  current, 
leading  for  example  to  the  first  isolation  of  the  elements,  sodium 
and  potassium.  Faraday  showed  that  for  a  given  substance  the 
amount  decomposed  is  dependent  solely  on  the  quantity  of 
electricity  passed  through  and  that  for  different  substances  the 


PHYSICAL  SCIENCE  IN  THE  NINETEENTH  CENTURY     365 

amounts  set  free  at  the  electrodes  are  proportional  to  their 
chemical  equivalents.  To  him  the  name  electrolysis  is  due.  A 
closer  study  of  the  phenomena  of  electrolysis  led  Clausius  to  the 
hypothesis  that  the  molecules  of  salts,  acids,  and  bases,  pre- 
viously regarded  as  disintegrated  only  by  the  passage  of  the 
electric  current,  are  already  dissociated  in  ordinary  solutions. 
To  these  electrically  charged  part-molecules  Faraday  gave  the 
name  ions.  Arrhenius  proved  that  salts  in  dilute  solution  are 
dissociated  into  then*  ions  almost  completely,  instead  of  only 
very  slightly  as  Clausius  supposed.  This  theory  of  Arrhenius, 
known  as  the  Theory  of  Electrolytic  Dissociation,  of  which  an 
account  would  be  too  technical  for  the  present  purpose,  co- 
ordinates and  correlates  heterogeneous  masses  of  chemical  facts, 
which  apparently  bore  little  or  no  relation  to  one  another,  and 
refers  them  to  a  common  cause. 

During  the  latter  part  of  the  nineteenth  century  a  study  of  the 
rate  and  equilibrium  conditions  of  chemical  reactions  led  by  de- 
grees to  the  formulation  of  the  so-called  law  of  mass  action  and  to 
many  important  thermodynamic  relations.  Chemistry  thus  came 
to  share  with  physics  the  possibility  of  utilizing  the  calculus, 
becoming  thereby  more  fully  a  quantitative  science. 

REFERENCES  FOR  READING 

MERZ,  J.  T.     History  of  European  Thought  in  the  Nineteenth  Century. 

POINCARE,  H.     Science  and  Hypothesis. 

RAMSAY,  WILLIAM.     The  Gases  of  the  Atmosphere  and  the  History  of  Their 

Discovery. 

ROSCOE,  H.  E.     John  Dalton. 
SODDY,  F.     Matter  and  Energy. 

THOMPSON,  S.  P.     Michael  Faraday:  His  Life  and  Work. 
TILDEN,  W.  A.     Progress  of  Scientific  Chemistry  in  Our  Own  Time. 
TYNDALL,  JOHN.    Faraday  as  a  Discoverer. 


CHAPTER  XVII 

SOME    ADVANCES    IN   NATURAL    SCIENCE   IN    THE    NINE- 
TEENTH   CENTURY.     COSMOGONY   AND    EVOLUTION 

What  the  classical  renaissance  was  to  men  of  the  fifteenth  and 
sixteenth  centuries,  the  scientific  movement  is  to  us.  It  has  given 
a  new  trend  to  education.  It  has  changed  the  outlook  of  the  mind. 
It  has  given  a  new  intellectual  background  to  life.  —  Sadler. 

The  rapid  increase  of  natural  knowledge,  which  is  the  chief  char- 
acteristic of  our  age,  is  effected  in  various  ways.  The  main  army  of 
science  moves  to  the  conquest  of  new  worlds  slowly  and  surely,  nor 
ever  cedes  an  inch  of  the  territory  gained.  But  the  advance  is  covered 
and  facilitated  by  the  ceaseless  activity  of  clouds  of  light  troops 
provided  with  a  weapon  —  always  efficient,  if  not  always  an  arm  of 
precision  —  the  scientific  imagination.  It  is  the  business  of  these 
enfants  perdus  of  science  to  make  raids  into  the  realm  of  ignorance 
wherever  they  see,  or  think  they  see,  a  chance;  and  cheerfully  to 
accept  defeat,  or  it  may  be  annihilation,  as  the  reward  of  error. 
Unfortunately  the  public,  which  watches  the  progress  of  the  cam- 
paign, too  often  mistakes  a  dashing  incursion  .  .  .  for  a  forward 
movement  of  the  main  body;  fondly  imagining  that  the  strategic 
movement  to  the  rear,  which  occasionally  follows,  indicates  a  battle 
lost  by  science.  —  Huxley. 

INFLUENCE  OF  EIGHTEENTH  CENTURY  REVOLUTIONS.  —  If  the 
French  Revolution  had  done  no  more  than  to  upset  as  it  did  the 
social  equilibrium  of  the  centuries,  its  effect  in  stimulating  inquiry 
and  generating  doubt  in  almost  every  direction  could  not  have 
failed  to  further  scientific  studies  and  promote  wholesome  investi- 
gation into  the  fundamental  relations  of  man  and  nature.  But 
even  before  that  revolution,  some  of  the  ablest  minds  in  France, 
keenly  alive  to  the  teachings  of  Descartes  and  Newton  and  the 
lessons  of  seventeenth  century  science,  had  rejected  the  cur- 
rent cosmogony  of  Moses,  although  they  had  nothing  with  which 
to  replace  it.  In  particular,  the  eighteenth  century  questioned 
all  custom  and  authority,  and  the  theory  of  special  creation 
possessed  no  other  basis. 

366 


NATURAL  SCIENCE  IN  THE  NINETEENTH  CENTURY     367 

The  American  Revolution  was  likewise  an  uprising  against 
long  established  custom  and  authority,  and  accordingly  contrib- 
uted to  the  doubts  and  questionings  of  the  time,  while  the 
Industrial  Revolution,  by  fundamental  and  world-wide  changes, 
such  as  the  introduction  of  machinery  and  the  factory  system, 
and  by  its  tendency  to  concentrate  and  urbanize  populations 
previously  rural  and  segregated,  facilitated  intellectual  contact, 
promoted  discussion,  and  aroused  and  excited  inquiry  and  in- 
vestigation. 

THE  SCIENTIFIC  REVOLUTION.  —  The  most  brilliant  single 
achievement  of  nineteenth  century  science  was  the  detection  by 
Adams  and  Leverrier  of  the  presence  in  our  solar  system  of  Nep- 
tune, a  new  and  hitherto  unknown  planet.  But  the  most  revolu- 
tionary achievement,  and  probably  the  most  far-reaching,  was  the 
assembling  and  formulation  of  convincing  evidence  in  favor  of 
organic  evolution,  i.e.  of  the  gradual  development,  rather  than 
the  sudden  creation,  of  living  things.  It  is  difficult  to-day  to 
realize  the  commotion  into  which  the  intellectual  world  was 
thrown  at  the  middle  of  the  nineteenth  century  when  a  new  and 
promising  solution  of  the  long-standing  problem  of  the  origin  of 
the  different  kinds  (species)  of  plants  and  animals  by  means  of 
natural  rather  than  supernatural  law,  was  propounded  by  Darwin 
and  Wallace.  And  while  the  last  half  of  the  eighteenth  cen- 
tury was  the  period  of  great  political  and  social  revolutions, — 
the  French,  the  American,  and  the  Industrial,  —  the  last  half 
of  the  nineteenth  century  experienced,  in  its  acceptance  of  a  new 
cosmogony,  a  fourth,  even  more  profound  and  momentous,  the 
Scientific  Revolution.  The  discovery  of  Neptune  was  a  triumph 
of  mathematics  and  astronomy,  the  establishment  of  the  theory 
of  organic  evolution,  a  triumph  of  biology.  The  discovery  of 
Adams  and  Leverrier  was  immediately  accepted  and  everywhere 
applauded,  but  the  ideas  broached  by  Darwin  and  his  collabo- 
rators encountered  widespread  and  powerful  opposition,  and  were 
accepted  only  tardily  and  reluctantly. 

INFLUENCE  OF  THE  RAPID  INCREASE  OF  KNOWLEDGE.  —  The 
invention  of  printing,  the  discovery  of  the  new  world,  and  the  works 


368  A  SHORT  HISTORY  OF  SCIENCE 

of  such  intellectual  giants  as  Galileo,  Kepler,  and  Newton,  followed 
as  these  were  by  the  rapid  increase  of  knowledge,  both  of  nature 
and  of  man,  in  the  seventeenth  and  eighteenth  centuries,  had 
placed  within  the  reach  of  all  a  vast  amount  of  new  facts  touching 
the  familiar  heavens  and  the  familiar  earth.  Moreover,  these 
facts  were  mostly  capable  of  some  sort  of  rational  interpretation, 
i.e.  of  assignment  to  a  place  in  some  category  of  facts  or  phenomena 
already  understood  and  regarded  as  natural  rather  than  super- 
natural. In  short,  in  the  eighteenth  and  nineteenth  centuries 
the  stock  of  human  knowledge  had  been  not  only  rapidly  and  im- 
mensely enlarged  and  enriched,  but  at  the  same  time  more  or 
less  successfully  correlated  with  knowledge  previously  possessed 
and  valued.  Some  of  this  new  knowledge,  moreover,  was  so 
different  from  the  old  as  to  seem  like  a  fresh  revelation. 

GRADUAL  APPRECIATION  OF  THE  PERMANENCE  AND  SCOPE  OF 
NATURAL  LAW.  —  While  it  had  been  easy  hitherto  to  assume  the 
occasional  suspension  of,  or  interference  with,  the  ordinary  course 
of  events  by  supernatural  or  other  unseen  or  unknown  influences, 
it  gradually  became  clear  that  no  such  suspension  or  interference 
could  happen  without  upsetting  what  seemed  to  be  the  natural 
and  orderly  sequence  of  events,  —  what  we  now  call  "  the  order 
of  nature."  Hence  doubt  arose  in  many  minds  whether  such 
suspensions  or  interferences  do  in  fact  occur,  and  whether  fixed 
and  changeless  law  is  not  a  fundamental  phenomenon  of  nature. 
The  vastness  and  variety  also  of  the  heavens,  no  less  than  the 
order  conspicuous  in  a  mighty  system  so  nicely  balanced  and  so 
perfectly  correlated  as  must  be  the  cosmos  explored  and  described 
by  Copernicus,  Galileo,  Kepler,  Newton  and  their  successors, 
gradually  dawned  upon  the  human  intellect,  and  profoundly 
impressed  mankind. 

Moreover,  if  the  thoughtful  turned  from  the  contemplation 
of  the  macrocosm  —  the  heavens  —  and  the  revelations  of  the 
telescope,  to  the  microcosm  —  man,  —  the  labors  of  Vesalius  and 
the  Italian  anatomists,  and  of  Harvey  and  the  microscopists, 
served  to  show  that  here  also  law  and  order  and  a  kind  of  mechan- 
ical regularity  and  perfection  held  sway,  while  plants  and  the  lower 


NATURAL  SCIENCE  IN  THE  NINETEENTH  CENTURY     369 

animals  had  long  been  observed  to  be  strictly  obedient  to  and 
dependent  upon  the  laws  of  nature  in  respect  to  climate,  season, 
food,  reproduction,  etc. 

NATURAL  THEOLOGY  AND  AN  AGE  OF  REASON.  —  At  the  end  of 
the  seventeenth  century  John  Ray,  an  English  zoologist,  drew 
attention  to  the  remarkable  adaptations  everywhere  discover- 
able in  nature  and  especially  in  plants  and  animals,  and  suggested 
that  these  adaptations  were  sufficient  to  prove  the  existence  of 
"design"  in  the  universe,  —  a  powerful  argument  in  favor  of  the 
Mosaic  cosmogony.  The  same  idea  was  urged  more  at  length  by 
others  in  the  eighteenth  century  as  an  offset  to  the  growing  scep- 
ticism of  the  age,  and  especially  by  Butler  in  his  great  work  on 
the  Analogy  of  Religion,  Natural  and  Revealed,  to  the  Course  and 
Constitution  of  Nature  (1736),  and  by  Paley  in  his  famous  Nat- 
ural Theology  (1802).  More  popular  and  more  radical  influences 
were  simultaneously  at  work  in  the  opposite  direction,  as  for 
example,  Paine's  Rights  of  Man  and  Age  of  Reason,  while 
Gibbon  with  prodigious  learning,  and  Hume  with  searching  philo- 
sophical criticism,  added  to  the  increasing  dissatisfaction  of  the 
thoughtful  with  the  current  cosmogony,  —  a  dissatisfaction 
which  had  been  rapidly  growing  under  the  doctrine  of  the  neces- 
sity of  doubt  emphasized  by  Descartes. 

Between  1842  and  1846  appeared  a  revolutionary  work  entitled 
Vestiges  of  Creation,  by  an  anonymous  author,  which  aroused  in- 
tense interest  in  scientific  circles  and  a  storm  of  criticism  from  those 
who  held  to  the  old  cosmogony.  It  is  now  known  to  have  been 
written  by  Robert  Chambers,  an  Edinburgh  publisher  who  pre- 
ferred to  remain  unknown  from  fear  of  injuring  his  partners  by 
bringing  down  upon  them  the  wrath  of  critics  for  his  heterodoxy. 
Chambers  was  an  amateur  geologist  and  in  his  "  Vestiges  "  under- 
takes to  treat  the  genesis  of  the  earth  on  more  rational  and  more 
natural  principles  than  was  possible  by  following  the  orthodox 
theory  of  special  creation. 

The  publication  of  Darwin's  Origin  of  Species  in  1859  re- 
sulted, after  a  period  of  earnest  and  sometimes  acrimonious 
discussion,  in  the  establishment  of  what  is  now  known  as  the 
2n 


370  A  SHORT  HISTORY  OF  SCIENCE 

theory  or  doctrine  of  organic  evolution,  and  in  the  displacement  of 
the  prevailing  theory  of  special  creation,  —  a  forward  step  which 
removed  the  principal  stumbling-block  in  the  way  of  acceptance 
of  the  theory  of  general  evolution,  inorganic  as  well  as  organic, 
telluric  as  well  as  stellar.  In  other  words,  Darwin's  work  at  one 
blow  cleared  the  way  for  a  new  cosmogony. 

NATURAL  PHILOSOPHY  AND  NATURAL  HISTORY.  DIFFEREN- 
TIATION AND  HYBRIDIZING  OF  THE  SCIENCES.  —  Mathematics, 
always  recognized  as  a  principal  branch  of  the  tree  of  learning, 
at  the  beginning  of  the  nineteenth  century  still  held  its  place  as  the 
mother  of  the  sciences.  Astronomy,  also,  often  called  the  queen 
of  the  sciences,  still  occupied  its  ancient  and  honorable  position, 
having  by  this  time  lost  all  traces  of  discreditable  affiliation  with 
astrology.  With  the  physical  and  natural  sciences,  as  we  now 
know  them,  the  case  was  different.  These  still  existed  in  a  com- 
paratively amorphous  and  largely  undifferentiated  condition  as 
"natural  philosophy"  and  "natural  history," — the  former  the 
lineal  descendant  of  the  Ionian  nature  philosophy,  now  promoted  to 
a  high  place  in  public  esteem  by  the  work  of  Newton,  whose  great 
Principia  were  philosophiae  naturalis.  Gradually,  as  time  went 
on,  chemistry  was  more  and  more  differentiated  from  natural 
philosophy,  until  about  1875  it  became  customary  to  drop  the 
term  natural  philosophy,  using  instead  two  terms,  chemistry  and 
physics.  By  the  end  of  the  century  the  present  practice  was  fully 
established. 

The  primitive  condition  of  the  natural  history  sciences  at  the 
beginning  of  the  century  may  be  inferred  from  the  remark  of  an 
eminent  geologist  (Geikie)  that  at  that  time  geology  and  biology 
were  not  yet  inductive  sciences.  By  1880,  however,  natural 
history  had  budded  off  geology,  botany,  zoology,  and  physiology 
as  independent  sciences,  and  the  parent  term,  though  still  em- 
ployed, was  rapidly  falling  into  disuse,  having  become  much  too 
broad  for  any  single  science. 

Meantime,  hybridizing  as  well  as  differentiation  has  become 
common,  e.g.  of  physics  with  chemistry  (physical  chemistry), 
and  of  mathematics  with  physics  (mathematical  physics)  and  with 


NATURAL  SCIENCE  IN  THE  NINETEENTH  CENTURY     371 

many  other  sciences.  We  now  have  also  fertile  hybrids  between 
chemistry  and  biology  (physiological  chemistry,  bio-chemistry, 
chemical  biology,  etc.),  and  between  physics  and  geology  (geo- 
physics), between  electricity  and  chemistry  (electro-chemistry), 
between  physics  and  mineralogy,  etc.  Hybridizing  of  this  kind 
is  one  of  the  most  characteristic  as  well  as  one  of  the  most  fruit- 
ful phenomena  of  the  nineteenth  century. 

Botany,  zoology  and  geology,  daughters  of  natural  history, 
were  the  children  of  its  old  age,  for  the  term  "  natural  history  "  is 
as  ancient  as  Aristotle,  while  geology  was  not  fully  born  until  the 
publication  of  Ly ell's  Principles  in  1830,  and  biology  not  until 
the  era  of  the  great  generalists  of  the  Victorian  Age  —  Darwin, 
Spencer,  Huxley,  etc.  —  soon  after  the  middle  of  what  one  of 
them,  Wallace,  well  qualified  by  his  own  great  work  to  speak 
with  authority,  has  called  "the  wonderful  century."  Botany 
and  zoology  as  such  arose  about  the  beginning  of  the  century. 
Geology,  dealing  with  the  natural  history  of  the  earth  and  its 
lifeless  contents,  and  biology,  dealing  with  the  world  of  life,  have 
both  now  very  numerous  progeny,  e.g.  from  geology,  stratigraphy, 
mineralogy,  petrography,  petrology,  palaeontology,  etc.,  and  from 
biology,  zoology  and  botany,  with  their  numerous  subdivisions, 

—  morphology,  physiology,  cytology,  anthropology,  bacteriology, 
parasitology,    etc.     Here   also    highly   prolific    crossing   has   oc- 
curred both  among  members  of  each  minor  group  and  also  be- 
tween members  of  the  two  major  groups,  natural  philosophy  and 
natural  history;    as,  for  example,  in  palaeontology,  which  may 
be  said  to  be  half  geology  and  half  biology,   in  physiological 
optics,  in  bio-metrics,  etc.     To  the  very  beginning  of  the  century 
belongs  the  first  appearance  of  the  term  "  biology,"  introduced 
by  Treviranus  (1776-1837)  a  German  naturalist  and  professor 
of  mathematics  in  Bremen  who  in  1802-1805  published  a  work 
entitled  Biologie,  oder  Philosophic  der  lebenden  Natur. 

The  greatest  achievement  of  natural  history,  not  only  of  the 
nineteenth  century  but  of  all  time,  was  the  bringing  about  of  the 
general  acceptance  of  a  new  cosmogony  —  the  theory  of  evolution 

—  on  the  presentation  by  thfc  naturalist  Darwin  of  convincing 


372  A  SHORT  HISTORY  OF  SCIENCE 

evidence  in  favor  of  organic  evolution  together  with  a  plausible 
explanation  of  the  mechanism  (natural  selection)  of  its  operation. 
To  this  we  shall  return.  In  a  century  so  rich  and  so  varied  in 
its  achievements  in  natural  science  as  was  the  nineteenth,  we 
can  obviously  only  touch  —  and  that  very  briefly  —  upon  a  few 
of  the  more  important  and  fundamental. 

Of  the  remarkable  progress  of  all  the  sciences  during  the 
Victorian  era,  Huxley  has  given  the  best  brief  and  general  ac- 
count in  his  essay  entitled  Advance  of  Science  in  the  Last  Half 
Century  (1887),  prepared  in  celebration  of  the  first  fifty  years 
of  the  reign  of  Queen  Victoria. 

PROGRESS  IN  ZOOLOGY.  —  The  work  of  Buffon  and  Linnaeus 
in  the  field  of  biology  and  of  Werner  and  Hutton  and  Smith  in 
that  of  geology  has  been  referred  to  in  Chapter  XIV.  Of  these 
only  Werner  (d.  1817)  and  Smith  (d.  1839)  lived  on  into  the  nine- 
teenth century. 

The  return  of  the  astronomers  and  the  geologists  to  ancient 
ideas  of  gradual  development  or,  as  this  is  now  called,  evolution, 
for  the  lifeless  earth,  was  foreshadowed  for  the  living  world  with 
Bonnet  (1720-1793)  who  in  1764,  in  his  Contemplation  de  la  nature, 
advanced  the  theory  that  living  things  form  a  gradual  and  natural 
"scale"  (ladder),  rising  from  lowest  to  highest  without  any  break 
in  continuity.  Buffon,  in  his  great  work  on  natural  history,  which, 
was  published  between  1749-1804  in  44  quarto  volumes,  had 
dealt  with  the  animal  world  very  much  as  Linnaeus  had  dealt 
with  plants,  Buffon  excelling  in  description,  Linnaeus  both  in 
description  and  in  classification  and  holding  firmly  to  the  idea  of 
the  fixity  as  well  as  the  definite  demarcation  of  species. 

Meantime,  epoch-making  work  in  zoology  was  being  done  by 
three  investigators  —  Lamarck,  Cuvier,  and  St.  Hilaire  —  at  the 
Museum  of  Natural  History  in  Paris.  In  1778  Lamarck  (1744- 
1829)  published  a  small  book  on  botany.  In  1801  appeared 
Ms  great  work  On  the  Organization  of  Living  Bodies,  which  is 
now  a  landmark  in  the  history  of  biology  and  of  the  doctrine  of 
organic  evolution.  In  this  work  and  in  his  Philosophie  zoologique, 
Lamarck  boldly  proposes  to  substitute  for  special  creation  — 


NATURAL  SCIENCE  IN  THE  NINETEENTH  CENTURY     373 

the  current  theory  of  cosmogony  —  the  idea  of  gradual  develop- 
ment or  evolution,  an  ancient  idea  thenceforward  made  the 
keynote  of  his  speculations.  Systematic  zoology  and  compara- 
tive anatomy,  the  latter  already  well  begun  by  Hunter  in  the 
eighteenth  century,  were  immensely  advanced  by  Cuvier  (1769- 
1832),  who  however  clung  tenaciously  to  the  theory  of  special 
creation;  while  Geoffrey  St.  Hilaire  (1772-1844)  —  also  a  com- 
parative anatomist,  but  one  whose  interests  lay  rather  in  the 
functional  than  in  the  anatomical  resemblances  of  the  parts  of 
animals,  and  who  is  therefore  regarded  as  "the  father  of  homol- 
°gy"  —  on  the  whole  opposed  Cuvier 's  and  favored  Lamarck's 
ideas.  His  Philosophie  anatomique  appeared  in  1818-1822. 

Nature,  said  St.  Hilaire,  has  formed  all  living  beings  on  one  plan, 
essentially  the  same  in  principle,  but  varied  in  a  thousand  ways  in  all 
the  minor  parts ;  all  the  differences  are  only  a  complication  and  modi- 
fication of  the  same  organs. 

This  similarity  of  structure,  or  homology  as  it  is  called,  which  runs 
through  all  animals,  was  thus  first  clearly  stated  by  St.  Hilaire,  and 
has  now  been  carefully  worked  out  and  confirmed.  .  .  .  Yet  Cuvier 
opposed  it  to  the  last,  for  his  mind  was  full  of  another  idea  which  is 
equally  true ;  namely,  how  perfectly  each  part  of  an  animal  is  made 
to  fit  all  the  other  parts ;  and  it  seemed  to  him  impossible  that  this 
could  be,  unless  each  part  was  created  expressly  for  the  work  it  had 
to  do. 

The  discussion  between  the  two  friends  became  so  animated  that 
all  Europe  was  excited  by  it.  It  is  said  that  Goethe,  then  an  old 
man  of  eighty-one,  meeting  a  friend,  exclaimed,  'Well,  what  do  you 
think  of  this  great  event  ?  the  volcano  has  burst  forth,  all  is  in  flames. ' 
His  friend  thought  he  spoke  of  the  French  Revolution  of  July,  1830, 
which  had  just  occurred,  and  he  answered  accordingly.  '  You  do  not 
understand  me,'  said  Goethe, '  I  speak  of  the  discussion  between  Cuvier 
and  St.  Hilaire:  the  matter  is  of  the  highest  importance.  The 
method  of  looking  at  nature  which  St.  Hilaire  has  introduced  can 
now  never  be  lost  sight  of.'  —  Arabella  Buckley  Fisher. 

The  history  of  zoology  in  the  first  half  of  the  nineteenth  century 
is  chiefly  that  of  the  work  of  Cuvier,  St.  Hilaire,  Lamarck,  Agassiz 
and  their  disciples. 


374  A  SHORT  HISTORY  OF  SCIENCE 

PROGRESS  IN  BOTANY.  —  The  Linnsean  system  of  classification 
for  the  higher  plants  was  a  purely  empirical  system,  based  largely 
upon  the  number  of  stamens  and  not  involving  any  ideas  of  rela- 
tionship through  descent.  B.  de  Jussieu  (1699-1767),  a  friend  and 
pupil  of  Linnaeus,  had  proposed  a  different  system  of  classifica- 
tion in  which  weight  is  given  to  the  totality  of  resemblances  of 
whatever  kind,  and  this,  which  almost  inevitably  led  to  the  close 
association  of  related  forms,  was  an  important  step  toward  a 
natural  classification,  i.e.  one  based  avowedly  upon  relationship, 
common  ancestry,  or  descent.  De  Jussieu's  nephew  Antoine  de 
Jussieu  continued  and  extended  his  uncle's  work.  A.  de  Candolle 
(1778-1841)  later  adopted  and  extended  de  Jussieu's  system 
which,  with  his  own,  now  forms  the  basis  of  our  present  natural 
system.  It  is  noteworthy  that  this  change  of  opinion  in  regard 
to  the  relationship  of  the  species  of  plants  was  ultimately  effected 
without  theological  protest.1 

The  discovery  by  Goethe  of  the  homologies  of  the  parts,  and 
by  Linnaeus  of  the  organs  of  sex,  of  the  flower,  were  important 
steps  toward  the  modern  theory  of  the  evolution  of  plant  life. 

PROGRESS  IN  MICROSCOPY.  THE  ACHROMATIC  OBJECTIVE.  — 
Compound  microscopes,  i.e.  microscopes  consisting  of  two  lenses, 
an  objective  and  an  eyepiece,  were  probably  invented  at  about 
the  same  time  as  telescopes,  —  which  likewise  consist  of  two  lenses 
or  systems  of  lenses.  But  because  of  their  imperfections,  In 
respect  especially  to  spherical  and  chromatic  aberration,  such 
microscopes  were  often  inferior  for  use  to  the  best  simple  micro- 
scopes. It  was  not  until  about  1835  that  the  compound  micro- 
scope, though  invented  in  the  seventeenth  century,  became  the 
superior  instrument  that  it  is  to-day,  through  the  accumulated 
improvements  of  a  number  of  workers,  —  especially  Amici,  Lilly, 
Lister,  and  Chevalier  —  resulting  in  the  achromatic  objective, 
free  from  both  spherical  and  chromatic  aberration. 

Almost  immediately  thereafter,  with  the  new  microscopy, 
began  a  rich  harvest  of  discoveries,  in  what  Pasteur  has  called  the 

1  For  an  account  of  Linnaeus'  attitude  to  the  doctrine  of  the  fixity  of  species  see 
A.  D.  White,  Warfare  of  Science,  Vol.  I,  pp.  47,  59,  60. 


NATURAL  SCIENCE  IN  THE  NINETEENTH  CENTURY     375 

world  of  the  infinitely  little,  similar  to  that  reaped  after  the  intro- 
duction of  the  telescope  by  Galileo,  and  his  exploration  of  the 
stars,  in  the  world  of  the  infinitely  great.  The  cell  theory  of 
Schleiden  and  Schwann  appeared  in  1839  and  yeast  was  redis- 
covered (see  p.  378)  in  1837.  The  first  contagious  disease  (Mus- 
cardine)  traced  to  a  fungus  parasite  was  worked  out  by  Bassi 
in  1837,  the  first  contagious  disease  (Favus)  of  man  due  to  a 
fungus,  by  Schoenlein  in  1839.  Protoplasm  was  first  described  in 
1846.  Ehrenberg,  in  1838,  made  numerous  and  important  studies 
on  microscopic  plants  and  animals. 

EMBRYOLOGY.  —  If  in  1828  one  sharp  boundary  which  had 
always  been  supposed  to  stand  between  the  organic  and  the  in- 
organic world  was  broken  down  by  Wohler's  discovery  that  urea, 
a  substance  hitherto  exclusively  of  animal  origin,  could  be  ob- 
tained in  the  laboratory  by  heating  an  inorganic  substance, 
ammonium  cyanate,  another  well-defined  boundary  believed  to 
exist  between  the  higher  and  the  lower  animals  had  been  broken 
down  a  year  earlier,  when  a  Russian  zoologist,  Karl  Ernst  von 
Baer  (1792-1876),  announced  that  mammals,  including  man 
himself,  reproduce  by  eggs,  precisely  as  do  the  lower  animals. 
In  1828  von  Baer  published  our  first  important  work  on  compara- 
tive embryology,  —  of  which  science  he  thus  became  the  founder. 

The  discovery  by  von  Baer  of  the  human  ovum  overthrew 
completely  the  "animalculists"  who  for  centuries  had  contended 
that  within  the  earliest  embryo  of  man  the  future  offspring  existed 
completely  formed,  but  only  in  miniature.  This  theory,  because 
it  assumed  for  development  a  mere  unfolding,  was  known  as  em- 
bryologic  evolution.  Harvey,  on  the  other  hand,  had  propounded 
a  theory  of  epigenesis,  i.e.  development  comprising  growth  and 
differentiation  out  of  an  originally  minute,  simple,  and  undiffer- 
entiated  body.  This  "body"  —  the  human  ovum  —  was  now 
described  by  von  Baer  as  -g^  inch  in  diameter  and  nowise  different 
in  appearance  from  other  animal  eggs  in  their  earliest  stages. 
Comparative  anatomy  had  already  shown  that  Linnaeus  was 
right  in  placing  man  among  the  animals,  and  now  embryology  con- 
firmed and  strengthened  this  view  of  man's  place  in  nature. 


376  A  SHORT  HISTORY  OF  SCIENCE 

PROGRESS  IN  PHYSIOLOGY.  JOHANNES  MULLER.  CLAUDE 
BERNARD.  —  To  the  work  upon  physiology  of  Harvey  in  the 
seventeenth  century  and  of  Haller  and  Bichat  and  others  in  the 
eighteenth  was  now  added  that  of  Johannes  Muller  (1801-1858) 
whose  "Elements  of  Physiology,"  appearing  between  1837  and 
1840,  put  the  whole  subject  on  a  fresh  and  thoroughly  scientific 
basis.  Muller  has  been  called  the  founder  of  modern  physiology. 
Fortunate  in  his  pupils  —  DuBois  Reymond,  Helmholtz,  Ludwig, 
Volkmann,  and  Vierordt  —  these  were  no  less  fortunate  in  their 
master,  for  Muller  was  a  great  teacher,  and  for  the  rest  of  the 
century  the  teachings  of  Johannes  Muller  and  his  disciples  fur- 
nished a  powerful  stimulus  and  a  safe  guide  to  physiological 
research,  especially  in  Germany. 

In  France,  also,  physiology  won  renown  and  recognition  through 
the  researches  of  Claude  Bernard  (1813-1878),  a  pupil  of 
Magendie,  whose  assistant  he  became  in  1841  and  whom  he  suc- 
ceeded as  assistant  professor  in  1847  and  as  professor  in  1855. 
Bernard  was  the  first  occupant  of  the  newly  established  chair 
of  physiology  at  the  Sorbonne.  The  laboratory  was  attached  to 
his  professorship  until  1864.  On  his  death  in  1878  he  was  accorded 
by  the  State  the  honor  of  a  public  funeral,  —  the  first  ever  be- 
stowed by  France  upon  a  man  of  science  and  only  84  years  after 
the  public  guillotining  of  Lavoisier.  By  his  discovery  of  the 
significance  of  the  pancreatic  secretion  and  especially  of  the  glyco- 
genic  function  of  the  liver  Bernard  opened  up  the  vast  field  of 
"internal  secretions,"  the  study  of  which  has  yielded,  and  is  still 
yielding,  some  of  the  most  fruitful  results  of  physiological  research 
hitherto  obtained.  Before  Bernard,  each  organ  seemed  to  have 
one  function  and  only  one,  but  since  his  tune  this  simple,  mechan- 
ical concept  has  given  way  to  a  realization  of  correlations  and 
complexities  within  the  animal  mechanism  such  as  had  not  then 
been  dreamt  of. 

A  great  step  forward  in  this  dark  field  was  taken  in  1843  by  the 
French  physiologist,  Claude  Bernard,  a  man  whose  name  should 
be  remembered  for  his  striking  discoveries,  ingenious  and  skillful 
experiments,  his  clear  thoughts,  lofty  imagination  and  the  beautiful, 


NATURAL  SCIENCE  IN  THE  NINETEENTH  CENTURY     377 

simple  and  luminous  style  in  which  his  books  and  papers  were  written. 

—  Mathews. 

In  England  and  America  the  newer  physiology  made  but  scant 
progress  until  Foster  published  (in  1876)  in  England  an  epoch- 
making  treatise  embodying  in  a  fascinating  form  the  methods 
and  results  of  continental  physiology. 

PATHOLOGY  BEFORE  PASTEUR.  —  Before  the  nineteenth  cen- 
tury disease  was  regarded  as  an  inscrutable  mystery.  Epidemics, 
plagues,  and  pestilences  came  and  went,  without  apparent  rea- 
son. The  most  fatal  and  therefore  most  famous  of  these  was  the 
Black  Death  of  the  fourteenth  century.  Others  had  been  the 
Plague  of  Athens,  the  Sweating  Sickness,  the  Dancing  Mania,  and 
Leprosy.  One  of  the  worst  and  commonest  was  Scurvy,  which 
attacked  chiefly  sailors,  soldiers,  prisoners  and  the  poor. 

Attempts  to  explain  disease  were  manifold.  Primitive  man 
naturally  attributed  it  to  the  power  of  evil  spirits  (daemons  or 
devils)  and  sought  prevention  and  cure  in  exorcism  and  the  casting 
out  of  devils.  Hippocrates  looked  for  the  sources  of  disease  in 
abnormal  mixtures  of  four  great  juices  or  "humors"  of  the  body, 

—  blood,  yellow  bile,  phlegm,  and  black  bile ;  and  his  theory  had 
the  merit  of  being  based  upon  natural  rather  than  supernatural 
ideas,  for  which  reason  probably  it  survived  until  the  time  of 
Sydenham  in  the  seventeenth  century.     But  the  theory  of  Hip- 
pocrates failed  to  account  for  epidemics,  for  which  the  cause  had 
to  be  sought  in  meteorological  disturbances,  such  as  storms,  or  in 
astronomical  phenomena,  such  as  comets  or  eclipses,  or  in  unusual 
terrestrial  happenings,  such  as  earthquakes,  volcanic  eruptions, 
the  flight  of  birds,  the  appearance  of  insects,  vermin  and  what  not. 
With  the  increase  of  knowledge  in  the  sixteenth  and  seventeenth 
centuries  ideas  of  this  primitive  kind  no  longer  sufficed,  and 
Sydenham  urged  that  disease  must  have  an  independent  material 
basis,  a  materies  morbi.    Not  much  progress  was  made,  how- 
ever, even  by  Sydenham,  and  the  eighteenth  century  left  behind 
it  no  important  contributions  to  the  theory  of  disease,  —  the  work 
of  Hahnemann,  for  example,  bearing  upon  therapeutics  rather 
than  pathology. 


378  A  SHORT  HISTORY  OF  SCIENCE 

The  nineteenth  century  began  as  a  period  of  agnosticism  in 
pathology.  The  older  theories  were  discredited,  but  beyond  a 
general  belief  in  the  material  basis  of  the  agencies  of  disease 
almost  nothing  was  known.  Scurvy,  indeed,  had  been  shown 
to  be  due  to  lack  of  certain  kinds  of  food,  and  smallpox  had  been 
proved  to  be  preventable  both  by  inoculation  and  vaccination. 
Boyle,  in  the  seventeenth  century,  had  ventured  the  guess  that 
diseases  might  be  "fermentations,"  but  as  fermentations  were 
not  yet  understood  the  suggestion  had  little  value.  Light  finally 
came  from  two  sources,  viz.,  from  parasitology  and  from  zymology, 
—  the  science  of  fermentations.  It  had  long  been  recognized  that 
the  mistletoe  was  a  parasite  causing  serious  disease  in  trees, 
and  that  tapeworms  might  cause  disease  in  animals  which  they 
infested.  It  was  not,  however,  until  the  microscope  came  into 
use  that  the  itch,  long  known  as  a  contagious  disease,  was  found 
to  be  due  to  a  parasitic  insect,  while  flies,  fleas,  bedbugs  and  lice 
were  still  thought  to  be  annoying  rather  than  dangerous.  The 
discovery  in  1837  that  "honeycomb"  of  the  scalp  (Favus),  an 
infectious  disease  in  which  yellow  crusts  appear  on  the  head,  is 
due  to  a  vegetable  parasite  related  to  the  moulds  was  a  surprise, 
as  was  the  demonstration  in  1839  that  an  infectious  disease 
(Muscardine)  of  silkworms  is  likewise  due  to  a  mould. 

The  microscope  also  served  to  reveal  what  have  been  called 
"  the  footprints  of  disease  "  within  the  cells  and  tissues,  making 
possible  the  work  in  cellular  pathology  by  Virchow. 

THE  GERM  THEORY  OF  FERMENTATION,  PUTREFACTION  AND 
DISEASE.  PASTEUR.  —  At  about  this  time  the  achromatic  com- 
pound microscope  was  coming  into  use,  and  by  its  aid  the  alco- 
holic fermentation,  hitherto  regarded  as  a  purely  chemical  phe- 
nomenon, was  found  to  be  intimately  associated  with,  if  not 
actually  caused  by,  a  living,  growing  microorganism,  yeast,  ob- 
served and  figured  by  Leeuwenhoek  in  1680,  but  in  the  early 
nineteenth  century  regarded  rather  as  potent  organic  matter  in 
some  peculiar  catalytic  state  or  condition  (Liebig)  than  as  a 
living  thing.  Between  the  rediscovery  of  yeast  in  1837  and 
Pasteur's  epoch-making  studies  upon  it  in  1859,  fermentation  was 


NATURAL  SCIENCE  IN  THE  NINETEENTH  CENTURY     379 

studied  by  several  workers  of  eminence  —  among  whom  was 
Helmholtz  —  but  it  was  chiefly  Pasteur  who  in  a  memorable  series 
of  researches  finally  proved  that  yeast  is  the  one  and  only  cause 
of  the  alcoholic  fermentation,  —  a  biological  or  "  germ "  theory 
of  fermentation,  thus  displacing  Liebig's  chemical  or  catalytic 
theory,  —  the  germ  in  this  case  being  yeast.  By  the  use  of  the 
microscope,  combined  with  new  and  ingenious  methods  of  culti- 
vation of  yeast  and  other  microbes,  Pasteur,  between  1859 
and  1865,  proved  beyond  doubt  that  yeast  is  the  agent  of  the 
alcoholic  fermentation  and  that  other  microbes  are  the  agents  of 
other  familiar  fermentations,  such  as  the  butyric  and  acetic.  His 
work  was  marked  by  remarkable  precision  and  refinement. 

From  a  germ  theory  of  normal  fermentations,  putrefactions, 
and  decay  it  was  a  short  step  to  a  germ  theory  of  undesirable  or 
abnormal  fermentations,  such  as  often  occur  in  brewing  and  wine 
making.  In  these  last,  the  microscope  revealed  to  Pasteur  the 
presence  of  strange  forms  foreign  to  the  ordinary  fermentation, 
and  evidently  wild  yeast,  moulds,  or  other  extraneous  microbes 
which  by  interfering  with  or  supplanting  the  normal  forms,  pro- 
duced disagreeable,  or  abnormal,  i.e.  "diseased",  beer  or  wine. 

Similarly,  it  was  only  a  second  step  from  the  diseases  of  wine 
and  beer  to  those  of  animals  and  man.  A  disastrous  epidemic 
disease  affecting  silkworms  in  the  south  of  France  at  this  time 
brought  to  Pasteur  an  urgent  request  that  he  should  make  an 
investigation.  "But,"  said  Pasteur,  "I  have  never  handled  a 
silkworm."  "So  much  the  better,"  said  Dumas,  the  chemist,  who 
insisted  that  he  should  thus  patriotically  enter  the  field  of  animal 
pathology.  Pasteur  yielded  and  spent  three  years  in  studies  upon 
the  silkworm  disease,  with  results  invaluable  to  science  and  espe- 
cially to  pathology. 

ANTISEPTIC  AND  ASEPTIC  SURGERY.  LISTER.  —  Meantime 
Lister,  an  English  surgeon  resident  in  Edinburgh,  led  on  by 
Pasteur's  researches,  introduced  a  new  and  scientific  treatment  of 
open  wounds,  based  on  the  germ  theory.  Open  wounds  whether 
made  by  accident  or  in  surgery  ordinarily  suppurate,  i.e.  become 
red,  swollen  and  inflamed  and  eventually  produce  pus.  Lister 


380  A  SHORT  HISTORY  OF  SCIENCE 

surmised  that  this  suppuration  is  due  to  germs  from  the  air,  from 
the  surgeon's  hands,  from  instruments,  etc.,  and  acting  on  this 
theory  proposed  to  prevent  such  wound  diseases  by  destroying  the 
germs  in  the  air  and  upon  the  wound  by  some  "  antiseptic,"  i.e.  some 
substance  that  should  prevent  sepsis  (putrefaction)  or  suppuration. 
Carbolic  acid  (phenol)  had  recently  been  introduced  into  com- 
merce and  was  highly  recommended  as  a  deodorant.  This  Lister 
used,  and  with  results  so  satisfactory  that  his  antiseptic  surgery 
soon  became  famous.  It  has  since  given  way  to  aseptic  surgery, 
which  differs  from  it  simply  in  preventing  wound-infection  rather 
than  in  treating  it  after  it  has  occurred.  In  battle-fields  antiseptic 
surgery  must  still  be  used,  since  the  work  of  the  surgeon  is  done 
only  after  the  wound  has  been  made.  Antiseptic  and  aseptic 
surgery  are  among  the  most  priceless  blessings  of  the  race  and 
among  the  greatest  triumphs  of  nineteenth  century  science. 

One  serious  objection  stood  in  the  way  of  the  establishment  and 
acceptance  of  the  germ  theory;  viz.,  the  possibility  that  germs 
were  the  consequence  and  not  the  cause  of  fermentation,  putre- 
faction, or  disease ;  and  this  objection  was  frequently  urged.  In 
1876,  however,  it  was  met  and  overcome  by  Robert  Koch,  a 
district  physician  of  Wollstein,  in  Prussia.  By  the  use  of  the 
methods  of  Pasteur,  Koch  succeeded  in  making  a  series  of  suc- 
cessive cultivations  of  the  microbes  of  anthrax  (splenic  fever, 
charbm,  or  malignant  pustule)  in  such  a  way  that  at  the  end  of 
his  experiment  he  had  a  pure  culture  of  the  microbes  in  question. 
Obviously,  if  with  these  he  could  produce  the  disease  by  infecting 
a  susceptible  animal  or  a  wound,  they  must  be  its  cause  and  not 
its  consequence.  In  this  he  was  completely  successful,  thereby 
establishing  beyond  all  possible  peradventure  the  truth  of  the 
germ  theory. 

RISE  OF  BACTERIOLOGY  AND  PARASITOLOGY.  —  The  labors  of 
Pasteur,  Lister,  Koch  and  others  soon  led  to  the  birth  of  a  new 
science,  —  Bacteriology  —  of  which  the  first  fruit  was  the  dis- 
covery in  rapid  succession  by  Koch  and  his  pupils  of  the  hitherto 
unknown  germs  of  some  of  the  worst  and  most  mysterious  dis- 
eases afflicting  the  human  race ;  the  bacillus  of  typhoid  fever  in 


NATURAL  SCIENCE  IN  THE  NINETEENTH  CENTURY     381 

1879,  —  more  fully  worked  out  in  1884 ;  the  bacillus  of  tuberculosis 
in  1882 ;  the  vibrio  of  Asiatic  cholera  in  1883 ;  the  bacilli  of  lock- 
jaw and  of  diphtheria  in  1884 ;  the  bacillus  of  bubonic  plague  in 
1894 ;  and  about  the  same  time  by  others  of  the  microorganisms 
of  malaria,  sleeping  sickness,  and  several  other  diseases. 

In  some  cases  such  as  smallpox  and  yellow  fever  no  germs  have 
yet  been  observed ;  but  this  seems  at  present  to  be  because  they 
are  too  small  to  be  seen  with  the  microscope  or  to  be  held  back, 
as  most  germs  are,  by  pipe-clay  filters.  If,  nevertheless,  we  review 
the  list  just  given  of  those  plagues  in  which  the  causative  micro- 
organism was  detected  and  cultivated  between  1879  and  1889,  we 
cannot  avoid  the  conclusion  that  the  ninth  decade  of  the  nine- 
teenth century  was  the  most  important  hitherto  in  the  history  of 
pathology.  When  we  go  further,  and  compare  these  rich  dis- 
coveries and  the  fruit  they  have  since  borne,  in  preventive  medi- 
cine, preventive  sanitation  and  preventive  hygiene,  with  our 
previous  ignorance  of  the  nature  of  disease  and  of  its  control,  we 
realize  that  since  that  decade  the  world  has  possessed  not  only  a 
new  pathology  but  also  a  new  science. 

Besides  bacteriology  another  science,  parasitology,  has  also 
become  prominent  since  the  decade  of  the  great  pathological 
discoveries.  The  parasitic  character  of  the  mistletoe,  the  tape- 
worm, the  flea,  the  louse,  the  mosquito  and  other  visible  pests 
was  long  ago  evident,  but  it  was  only  after  the  discoveries  of  Pas- 
teur and  Koch  and  their  disciples  were  fully  comprehended  that 
the  germ  theory  of  disease  was  seen  to  be  at  bottom  a  theory  of 
parasitism.  Thereupon  parasitology  assumed  a  new  place  and  a 
new  significance  as  a  branch  of  pathology. 

BIOGENESIS  versus  SPONTANEOUS  GENERATION.  —  The  ques- 
tion of  the  origin  and  beginnings  of  life  on  the  earth  has  always 
been  obscure  and  perplexing  to  mankind,  and  up  to  the  middle  of 
the  nineteenth  century  the  account  attributed  to  Moses,  —  the 
so-called  theory  of  special  creation,  —  was  still  predominant 
though  about  to  give  way  to  the  theory  of  evolution.  A  similar 
obscurity  veiled  the  beginnings  of  individual  life.  Omne  mvum 
ex  ovo  (all  life  from  the  egg)  was  the  motto  of  those  who  thought 


382  A  SHORT  HISTORY  OF  SCIENCE 

only  of  the  higher  animals.  Omne  vivum  ex  vivo  was  that  of  those 
who  held  that  living  things  come  only  from  antecedent  life,  even 
if  not  from  eggs.  Both  of  these  groups  were  biogenesists,  since 
they  maintained  that  living  things  come  only  from  other  living 
things.  Opposed  to  them  were  the  abiogenesists  who  disputed 
these  ideas  and  believed  in  "spontaneous"  generation  (abiogenesis), 
i.e.  in  the  origin  of  living  things  from  lifeless  or  non-living  matter. 

The  dispute  was  very  old,  Aristotle,  for  example,  having 
favored  the  idea  of  spontaneous  generation.  In  the  eighteenth 
century  Spallanzani  for  biogenesis  and  Needham  for  abiogenesis 
had  fought  over  again  the  ancient  battle.  Lamarck,  at  the  be- 
ginning of  the  nineteenth  century,  looked  with  favor  upon  abio- 
genesis. The  improved  microscope  of  that  century  seemed  at 
first  to  strengthen  the  evidence  for  spontaneous  generation  by 
revealing  almost  everywhere  the  presence  of  microbic  life,  and 
the  idea  of  an  apparently  easy  generation  of  new  life  was  wel- 
comed by  some  interested  in  evolution,  as  accounting  naturally 
rather  than  supernaturally  for  the  origin  of  life  in  general.  Mean- 
time, the  discovery  of  the  mammalian  ovum  by  von  Baer  in  1827 
had  somewhat  improved  the  position  of  the  biogenesists,  but  the 
whole  question  remained  open  and  unsettled  at  the  middle  of 
the  century  and  until  it  was  attacked  by  Pasteur,  who  was  thor- 
oughly equipped  with  the  most  exact  scientific  methods  of  the 
day.  For  the  details  of  the  struggle  in  which  Pasteur  battled  for 
biogenesis  we  must  refer  the  reader  to  the  Life  of  Pasteur,  by 
Radot,  and  to  TyndalFs  Floating  Matter  of  the  Air.  The  up- 
shot was  that  all  the  evidence  advanced  by  the  advocates  of 
spontaneous  generation  was  shown  by  Pasteur,  —  ably  seconded 
by  Tyndall,  —  to  be  due  to  defective  technique ;  for  when  such 
defects  were  corrected  no  evidence  remained  of  the  generation 
of  life  by  lifeless  matter.  Thus  was  triumphantly  closed,  at  least 
for  the  time,  one  of  the  most  ancient  of  controversies. 

Obviously,  the  question  of  a  possible  spontaneous  generation 
of  living  matter  from  lifeless  under  special  conditions  such  as 
may  have  existed  during  the  early  history  of  our  globe  remains 
open.  All  that  modern  science  has  done  is  to  controvert  such 


NATURAL  SCIENCE  IN  THE  NINETEENTH  CENTURY     383 

evidence  as  has  been  advanced  of  its  ordinary  and  frequent 
occurrence  under  such  natural  conditions  as  prevail  to-day. 

PROGRESS  OF  GEOLOGICAL  SCIENCE.  —  In  1785  Hutton,  to 
whom  we  have  already  briefly  referred,  presented  to  the  Royal 
Society  of  Edinburgh  a  paper  entitled  Theory  of  the  Earth,  or 
an  Investigation  of  the  Laws  Observable  in  the  Composition, 
Dissolution  and  Restoration  of  Land  upon  the  Globe  (p.  317). 

In  this  remarkable  work  the  doctrine  is  expounded  that  geology 
is  not  cosmogony,  but  must  confine  itself  to  the  study  of  the  materials 
of  the  earth ;  that  everywhere  evidence  may  be  seen  that  the  present 
rocks  of  the  earth's  surface  have  been  formed  out  of  the  waste  of 
older  rocks  .  .  .  that  every  portion  of  the  upraised  land  is  subject 
to  decay ;  and  that  this  decay  must  tend  to  advance  until  the  whole 
of  the  land  has  been  worn  away.  ...  In  some  of  these  broad  general- 
izations Hutton  was  anticipated  by  the  Italian  geologists;  but  to 
him  belongs  the  credit  of  having  first  perceived  their  mutual  relations 
and  combined  them  in  a  luminous  coherent  theory  everywhere  based 
upon  observation.  ...  It  is  by  his  Theory  of  the  Earth  that  Hutton 
will  be  remembered  with  reverence  while  geology  continues  to  be 
cultivated.  —  Geikie. 

In  the  early  part  of  the  nineteenth  century  it  was,  nevertheless, 
firmly  held  that  the  earth  had  undergone  various  "revolutions," 
"catastrophes"  and  the  like  which,  taken  together  with  the  Flood 
of  Noah,  were  sufficient  to  explain  its  present  surface  features,  such 
as  mountains,  valleys,  plains,  boulders,  caves,  deserts,  sea-coasts,  etc. 
These  views  were  summed  up  in  the  term  Catastrophism,  i.e.  that 

at  a  number  of  successive  epochs  —  of  which  the  age  of  Noah  was 
the  latest  —  great  revolutions  had  taken  place  on  the  earth's  surface ; 
that  during  each  of  these  cataclysms  all  living  things  were  destroyed ; 
and  that,  after  an  interval,  the  world  was  restocked  with  fresh  assem- 
blages of  plants  and  animals,  to  be  destroyed  in  turn  and  entombed 
in  the  strata  at  the  next  revolution.  — Judd. 

Moreover,  at  the  beginning  of  the  century  most  considerations 
of  the  earth  and  of  the  living  world  were  dominated  by  two  pre- 
conceived ideas :  first,  that  the  universe,  including  the  earth  and 
its  belongings,  had  originated  as  described  in  the  first  chapter  of 


384  A  SHORT  HISTORY  OF  SCIENCE 

Genesis,  and  second,  that  the  present  features  of  the  earth  are  to 
be  explained  chiefly  by  the  more  recent  Flood  of  Noah  described 
in  the  seventh  chapter. 

Before  geology  had  attained  to  the  position  of  an  inductive  science, 
it  was  customary  to  begin  all  investigations  into  the  history  of  the 
earth  by  propounding  or  adopting  some  more  or  less  fanciful  hypothe- 
sis in  explanation  of  the  origin  of  our  planet,  or  even  of  the  uni- 
verse. ...  To  the  illustrious  James  Hutton  (1785)  geologists  are 
indebted  for  strenuously  upholding  the  doctrine  that  it  is  no  part  of 
the  province  of  geology  to  discuss  the  origin  of  things.  He  taught 
them  that  in  the  materials  from  which  geological  evidence  is  to  be 
compiled  there  can  be  found  '  no  traces  of  a  beginning,  no  prospect  of 
an  end.'  —  Geikie. 

The  vast  deposits  of  sand,  gravel  and  clay,  with  the  embedded 
remains  of  contemporaneous  animal  and  vegetable  life  with  which 
they  (glacial  torrents)  everywhere  covered  the  plains,  were  viewed 
till  recently  solely  in  relation  to  the  Mosaic  narrative  of  a  universal 
deluge,  and  were  referred  implicitly  to  that  source.  —  Wilson. 

As  late  as  1823  Buckland,  a  distinguished  English  geologist, 
published  a  work  on  extinct  animals  from  a  Yorkshire  cavern 
entitled  Reliquaz  Diluviance.  As  for  plants  and  animals,  the  almost 
universal  opinion  was  that  these,  like  the  earth,  had  been  specially 
created  and  had  remained  ever  since  substantially  unchanged. 

As  for  the  crust  of  the  earth,  composed,  as  this  is  often  seen  to 
be  in  section,  of  unlike  layers,  it  was  a  long  time  before  the  current 
idea  of  sudden  creation  could  be  replaced  by  one  so  different  as 
that  of  slow  and  steady  deposition.  This  change,  however,  was 
finally  though  only  gradually  effected,  largely  through  actual 
observation  and  measurement  of  the  slow  deposits  of  rivers,  and 
other  geological  phenomena  of  to-day,  combined  with  Lyell's 
thesis  that  those  of  the  past  were  essentially  similar.  The  time 
element,  in  brief,  began  to  be  recognized  as  a  new  and  an  important 
factor  in  the  making  of  the  earth's  crust. 

Reference  has  been  made  above  to  Lyell's  revolutionary  trea- 
tise, The  Principles  of  Geology,  published  in  1830.  This  great 
work  which  adopted,  emphasized,  and  extended  the  works  of 


NATURAL  SCIENCE  IN  THE  NINETEENTH  CENTURY     385 

Hutton  and  Smith,  eventually  overthrew  catastrophism  and 
established  uniformitarianisin  in  its  place.  (See  Appendix  H.) 

GLACIERS  AND  GLACIAL  THEORIES.  —  The  occurrence  on  the 
earth's  surface,  and  even  on  mountain  tops,  of  boulders  evidently 
of  distant  rather  than  local  origin,  had  long  been  a  puzzle  even  to 
geologists.  The  primitive  hypothesis  of  their  deposit  during  the 
Flood  —  the  so-called  diluvial  theory  —  no  longer  sufficed  to 
satisfy  inquiring  minds,  and  equally  inadequate  was  the  idea  of 
von  Buch  that  boulders  had  been  thrown  up  like  cannon  shot  by 
volcanoes  and  had  fallen  where  found.  In  1837  Louis  Agassiz 
(1807-1873)  advanced  the  present  doctrine:  viz.  that  boulders 
have  been  deposited  after  the  melting  of  masses  of  ice  by  which 
they  weje  slowly  brought  from  a  distance.  Agassiz  supported 
this  ice  or  "glacial"  theory  by  personal  observations  and  studies 
of  the  glaciers  of  the  Alps,  and  eventually  propounded  that  gen- 
eral theory  of  glaciation  or  ice  caps  at  the  earth's  poles  which  is 
now  universally  accepted.  Few  theories  have  ever  proved  more 
satisfactory,  scientifically  speaking,  more  popular,  in  the  best 
sense,  or  more  productive  of  simple  explanations  of  widespread 
and  diverse  phenomena.  We  have  only  to  set  over  against  the 
glacial  the  diluvial  theory,  with  its  fatal  weakness  in  requiring  the 
transportation  by  water  of  huge  masses  of  rock  over  long  distances, 
or  the  projectile  theory,  with  its  requirement  of  showers  of  flying 
boulders  falling  almost  anywhere,  to  realize  the  simplicity  and 
adequacy  of  the  glacial  theory.  The  word  "  boulder,"  nevertheless, 
remains  as  a  reminder  of  the  diluvial  theory,  since  it  is  derived 
from  words  signifying  "the  noise  of  a  stone  in  a  stream." 

RISE  OF  PALEONTOLOGY.  —  Before  the  nineteenth  century 
precise  knowledge  of  extinct  animals  and  plants  was  almost  wholly 
wanting.  Fossils  had  indeed  been  observed  from  the  earliest 
times  but  although  occasionally  correctly  interpreted,  as  for  ex- 
ample by  Pythagoras  and  Xenophanes,  Leonardo  da  Vinci  and 
Palissy.  Hooke  (p.  268)  at  the  end  of  the  seventeenth  century  first 
made  the  important  suggestion  that  fossils  might  serve  as  indicators 
of  phases  in  the  earth's  history  and  as  proof  of  the  existence  at  one 
time  of  a  tropical  climate  in  England.  In  the  eighteenth  century 
2c 


386  A  SHORT  HISTORY  OF  SCIENCE 

these  ideas  were  developed  by  Woodward  and  others,  while  JV 
Gesner  introduced  into  geology  the  suggestion  of  great  age  for 
the  earth  by  estimating  the  time  required  for  the  elevation  of 
certain  fossiliferous  strata  in  the  Apennines  at  80,000  years. 
Buffon  in  France  speculated  upon  the  successive  emergence  and 
depression  of  the  continents,  and  Werner  in  Saxony  noted  in 
successive  formations  the  gradual  approach  of  extinct  forms  of 
life  towards  existing  forms. 

In  the  early  part  of  the  nineteenth  century  palaeontology  began 
to  take  on  its  modern  form.  Pallas  had,  indeed,  discovered  vast 
deposits  of  extinct  mammoths  and  rhinoceroses  in  Siberia  in 
1768-1774,  —  Blumenbach  had  distinguished  between  the  fossil 
mammoth  and  the  living  elephant  in  1780,  —  and  in  1793  the 
American  mastodon  was  recognized  as  different  from  both  fossil 
mammoth  and  living  elephant.  In  1793  Lamarck  recapitulated 
and  emphasized  the  methods  and  results  of  his  predecessors  and 
sought  to  account  for  the  phenomena,  partly  by  changes  in  the 
habits  and  partly  by  changes  in  habitat  of  extinct  forms,  modi- 
fications from  whatever  source  being  held  to  be  conserved  and 
accumulated  by  inheritance,  and  in  1800  Cuvier  published  an 
important  paper  on  fossil  and  living  elephants.  Not  long  after, 
remains  of  huge  extinct  reptiles  were  discovered :  of  the  ichthyo- 
saurus and  plesiosaurus  in  1821;  of  the  mososaurus  in  1822;  of 
fossil  crocodiles  in  France  in  1831 ;  of  the  iguanodon  in  1848. 
These  "finds"  opened  up  a  new  world  of  buried  ancient  life  almost 
beneath  our  feet  scarcely  inferior  in  interest  to  the  starry  world 
far  overhead,  which  had  so  long  excited  the  curiosity  and  won- 
der of  mankind. 

In  1854  in  the  caves  of  Belgium  were  found  remains  of  lions  and 
other  animals  (including  man)  which  were  obviously  unlike  the 
same  species  to-day,  and  have  ever  since  been  spoken  of  as  the 
"cave"  lion,  the  "cave"  tiger,  etc.  With  the  human  remains 
were  discovered  prehistoric  implements  testifying  both  to  the 
antiquity  of  man  and  to  the  superiority  of  the  cave  men  to  other 
cave  animals.  Fossil  ferns  and  other  plants  were  also  found,  and 
even  fossil  insects,  —  the  latter  often  in  a  remarkably  good  state 


NATURAL  SCIENCE  IN  THE  NINETEENTH  CENTURY     387 

of  preservation.  Here,  also,  recognition  of  the  time  element  be- 
came inevitable  and  subversive  of  the  idea  of  sudden  and  special 
creation.  Hitherto  belief  in  the  antiquity  of  man  was  excep- 
tional, and  proofs  of  such  antiquity  were  almost  wholly  wanting. 
This  discovery,  therefore,  was  profoundly  important  and  of  far- 
reaching  significance  not  only  in  palaeontology  but  also  in  the 
foundation  of  what  is  to-day  known  as  anthropology. 

ANCIENT  AND  MODERN  THEORIES  OF  COSMOGONY.  —  When 
the  wonder  and  curiosity  of  primitive  man  developed  into  specu- 
lation touching  his  origin,  or  the  origin  of  things  about  him,  or 
the  origin  of  the  visible  universe,  cosmogony  began.  Until  the 
middle  of  the  nineteenth  century  the  Jewish  or  Mosaic  cosmogony 
embodied  in  the  first  chapter  of  the  Hebrew  Scriptures,  and  ac- 
counting for  the  origin  of  the  cosmos,  both  organic  and  inorganic, 
by  a  sudden  and  special  creation,  was  almost  universally  accepted 
throughout  Christendom.  Recent  investigations  indicate  that 
this  theory  was  really  pre-Jewish  in  origin  and  probably  Baby- 
lonian. If  so,  a  cosmogony  long  antedating  Greek  theories  pre- 
vailed throughout  Christian  Europe  and  America  to  the  middle  of 
the  nineteenth  century.  In  the  seventeenth  century  even  Galileo, 
Kepler,  and  Newton  raised  no  question  of  its  essential  validity. 

Of  the  two  great  minds  of  the  seventeenth  century,  Newton  and 
Leibnitz,  both  profoundly  religious  as  well  as  philosophical,  one  pro- 
duced the  theory  of  gravitation  [and]  the  other  objected  to  that 
theory  as  subversive  of  natural  religion.  —  Asa  Gray. 

The  eighteenth_century  was  an  age  of  doubt.  Descartes,  who 
"doubted_jwhatever  could  be  doubtedT"  had  beenT  succeeded  bryr 
Voltaire  and  tEe  encyclojpsedists  in  France,  and  by  Hume  and 
Gibbon  in  England,  and  incredulity,  not  to  say  scepticism,  was  in 
the  air.  Yet  no  new  theory  of  cosmogony  appeared,  and  merely 
to  doubt  an  old  hypothesis  is  neither  to  destroy  nor  to  supplant 
it.  Observations,  ideas,  and  discoveries,  however,  had  long  been 
accumulating  and  were  now  multiplying,  which  were  destined  to 
undermine  the  Mosaic  theory  and  establish  something  very  dif- 
ferent, and  more  resembling  Greek  cosmogonies,  in  its  place. 


388  A  SHORT  HISTORY  OF  SCIENCE 

A  complete  cosmogony  should,  in  theory  at  least,  attempt  to 
account  both  for  the  origin  of  the  cosmos  and  for  its  present  as- 
pects. This  the  theory  of  special  creation  failed  to  do.  It  de- 
scribed the  origin  of  the  cosmos  at  a  period  evidently  remote,  — 
inasmuch  as  it  was  stated  elsewhere  in  the  Scriptures  that  many 
generations  had  come  and  gone  since  the  Creation,  —  but  was 
silent  as  to  any  essential  progress  or  modifications  in  the  mean- 
time. Hence,  for  those  accepting  special  creation  the  inference 
naturally  was  that  no  great  changes  either  in  the  heavens  or  in 
the  earth  had,  in  fact,  taken  place  since  the  initial  act  of  creation, 
and  that  the  present  aspect  of  the  cosmos  is  substantially  its 
primitive  aspect.  On  this  theory  mankind  and  other  living  things 
had  not  developed,  but  rather  stood  still  or  even  —  as  in  the  case 
of  "the  fall  of  man"  —  actually  retrograded  from  a  more  perfect 
type.  In  complete  contrast  with  this  ancient,  Oriental  theory 
the  modern  theory  of  Evolution,  making  no  pretence  to  solve 
the  problem  of  the  origin  of  the  cosmos,  attempts  only  to  explain 
some  of  its  present  aspects. 

RELATIONSHIP  OF  THE  HEAVENS  AND  THE  EARTH.  —  It  had  for 
centuries  been  taken  for  granted,  as  a  part  of  the  geocentric 
theory,  that  the  heavens  and  the  earth  had  little  if  anything  in 
common  —  the  earth  being  the  centre  of  things  and  of  first  impor- 
tance. Copernicus,  however,  had  shown  that  the  earth  is  inferior, 
and  tributary  to  the  sun,  while  his  great  successors  Galileo, 
Kepler,  and  Newton  had  proved  both  earth  and  sun  to  be  no  more 
than  members  of  a  huge  system  of  heavenly  bodies  strictly  corre- 
lated by  gravitation.  Hence,  when  Franklin  drew  down  light- 
ning from  the  terrestrial  heavens  and  the  spectroscopists  not  long 
after  proved  a  substantial  chemical  identity  between  the  earth 
and  celestial  bodies,  the  older  cosmogony  began  to  seem  both 
primitive  and  parochial. 

Above  all,  the  ideas  of  Kant  and  Laplace,  which  seemed  to 
indicate  not  merely  a  structural  and  material  kinship  between  the 
heavens  and  the  earth,  —  such  as  that  later  revealed  by  the 
spectroscope,  —  or  a  functional  similarity,  —  such  as  that  dis- 
covered by  Franklin,  —  but,  more  remarkable  than  either,  a 


NATURAL  SCIENCE  IN  THE  NINETEENTH  CENTURY     389 

family  relationship  through  a  common  ancestry,  weighed  heavily 
against  the  theory  of  special  and  separate  creation  by  an  ex- 
traneous will  in  remote  time,  with  no  provision  for  change  to  meet 
changing  conditions. 

THE  SCALE  OF  LIFE  AND  THE  PHASES  OF  LIFE.  —  It  had  often 
been  commented  upon  that  in  the  world  of  life  there  is  always 
present  and  requiring  explanation  what  Bonnet  called  the  "  scale 
of  life,"  i.e.  the  fact  that  plants  and  animals  not  only  differ  greatly 
in  structure  and  complexity,  but  that  both  may  be  arranged  in  a 
kind  of  ascending  or  descending  natural  scale  (ladder)  with  highly 
complex  forms  at  the  top  and  relatively  simple  ones  at  the  bot- 
tom. On  the  doctrine  of  special  creation  it  was  difficult  to  find 
any  reason  for  or  advantage  in  the  existence  of  such  a  scale, 
while  the  suggestion  was  obvious  that  the  higher  forms  had 
somehow  come  from  or  passed  through  lower  forms.  A  rapid 
modification  of  living  forms,  such  as  this  suggestion  required,  is 
obvious  in  everyday  life  being  exemplified  by  the  so-called  phases  of 
life,  —  in  which  infancy  makes  way  for  youth,  youth  for  maturity, 
and  maturity  for  age.  To  the  attentive  observer  living  matter 
appears  to  be  thus  forever  changing,  and  on  the  whole  progressing 
or  advancing  from  simplicity  to  complexity. 

In  this  respect  the  stellar  universe  at  first  sight  appears  very 
different,  for  here  permanence  rather  than  change  seems  to  pre- 
vail. As  for  the  earth,  changes,  indeed,  do  often  occur  and  some- 
times progressively,  as  in  erosion,  glacial  action,  and  the  work  of  the 
tides,  so  that  the  earth  seems  to  stand  in  this  respect  somewhere 
between  changing  and  advancing  organic  life  and  the  unchanging 
heavens.  When,  therefore,  the  idea  broached  by  Hutton  and 
Smith  at  the  end  of  the  eighteenth  century  that  the  surface  of  the 
earth  has  been  made  and  is  still  being  made  what  it  is  to-day,  not 
suddenly  and  once  for  all  by  special  creation  centuries  ago,  but 
gradually,  and  by  forces  and  processes  similar  to  those  now  acting, 
a  new  and  revolutionary  notion  of  the  genesis  of  the  earth's  crust 
arose,  and  one  contrary  to  the  idea  of  special  creation.  The  same 
idea  carried  further  and  developed  by  Lyell  in  1830  became  thence- 
forward all  important :  — 


390  A  SHORT  HISTORY  OF  SCIENCE 

Amid  all  the  revolutions  of  the  globe  the  economy  of  Nature  has 
been  uniform,  and  her  laws  are  the  only  things  that  have  resisted  the 
general  movement.  The  rivers  and  the  rocks,  the  seas  and  the  con- 
tinents have  been  changed  in  all  their  parts;  but  the  laws  which 
direct  those  changes,  and  the  rules  to  which  they  are  subject,  have 
remained  invariably  the  same.  —  Lyell's  Vol.  I,  Title  Page  Motto. 

GENERAL  RESEMBLANCE  OF  MAN  TO  THE  LOWER  ANIMALS.  — 
At  the  end  of  the  eighteenth  century  the  increase  of  knowledge 
nowhere  led  to  more  startling  revelations  than  in  comparative 
anatomy,  for  a  very  moderate  amount  of  dissection  of  the  various 
types  of  vertebrates  suffices  to  show  that  all  of  these,  —  including 
man  himself,  —  are  built  upon  the  same  general  plan.  Similarity 
extends  even  into  minute  details,  as  in  the  lungs,  aortic  arches, 
teeth,  eyes  and  ears,  and  the  complex  musculature  of  the  limbs. 
Similarity  in  the  organs  and  processes  of  reproduction  among  the 
higher  animals  had  been  recognized  ever  since  the  time  of  Aris- 
totle, and  the  discovery  of  the  mammalian  ovum  by  von  Baer 
in  1827  simply  added  another  link  to  the  long  chain  of  resemblances 
between  man  and  other  higher  vertebrates  and  the  lower,  —  such 
as  reptiles,  frogs,  and  fishes.  Embryology  now  strengthened  this 
chain  by  showing  that  the  embryos  of  these  various  animals  are 
more  alike  than  are  the  adults  into  which  they  develop  —  thus 
suggesting  that  all  were  originally  similar  or  even  identical,  but 
had  afterwards  become  differentiated.  Malthus  in  his  startling 
work  on  the  Principle  of  Population  had  proved  a  tendency  in 
mankind  to  multiply,  like  other  animals,  without  reason  and 
beyond  the  means  of  subsistence.  The  antiquity  of  man,  long 
suspected,  was  established  by  the  finding,  in  1854,  by  Boucher  de 
Perthes,  of  human  remains  along  with  those  of  extinct  animals 
in  the  caves  of  northern  France.  Archaeology  and  linguistic 
studies  had  already  contributed  to  disprove  the  conventional 
chronology  (which  held  that  the  creation  of  the  world  occurred 
4004  B.C.)  and  thus,  indirectly,  the  current  cosmogony,  by  dis- 
covery of  the  remains  of  prehistoric  culture,  and  by  showing 
that  the  modern  European  languages  and  arts  are  evidently  direct 
and  related  descendants  of  earlier  and  sometimes  extinct  forms. 


NATURAL  SCIENCE  IN  THE  NINETEENTH  CENTURY     391 

ANATOMICAL  AND  MICROSCOPICAL  SIMILARITY  OF  ANIMALS 
AND  PLANTS.  ORGANS,  TISSUES,  CELLS,  AND  PROTOPLASMS. — 
The  old  cosmology  emphasized  differences  rather  than  resem- 
blances between  animals  and  plants  for,  barring  the  one  fact  of 
life,  there  is  at  first  sight  little  in  common  between  them.  It 
was  always  plain  that  both  are  provided  with  organs,  and  that  in 
respect  to  functions,  such  as  growth,  differentiation,  the  phases  of 
life  and  reproduction,  there  is  great  similarity.  The  improved 
microscope  of  1830-1850  now  revealed  a  further  and  striking  sim- 
ilarity, by  showing  that  the  organs  in  both  plants  and  animals 
are  made  up  of  tissues,  and  these  in  turn  of  cells ;  and  when  about 
1845  it  was  found  that  both  plant  and  animal  cells  contain  a  slimy, 
colorless  substance,  apparently  similar,  if  not  actually  identical, 
in  all  living  things,  it  was  not  long  before  the  same  name  "proto- 
plasm" (first  life)  was  given  to  this  fundamental  substance,  whether 
it  occurred  in  plant  or  in  animal  cells,  —  in  leaves  or  in  muscles. 
It  was  of  this  same  fundamental  protoplasm,  common  to  both 
plants  and  animals,  that  Huxley  wrote  his  famous  essay  entitled 
The  Physical  Basis  of  Life. 

FUNDAMENTAL  UNITY  OF  NATURE.  ORGANIC  versus  INORGANIC 
WORLD.  —  Between  things  organic  and  inorganic  until  the  nine- 
teenth century  there  was  supposed  to  be  a  great  gap.  When, 
therefore,  in  1828  Wohler  produced  in  the  laboratory  urea,  a 
typical  organic  substance  hitherto  unknown  except  as  an  animal 
excretion,  by  merely  heating  ammonium  cyanate,  it  became  evi- 
dent that  in  chemistry  the  term  "  organic  "  had  lost  its  former 
meaning.  Since  that  time  many  compounds  once  believed  to  be 
capable  of  production  only  by  living  things,  have  been  made 
in  the  laboratory,  with  the  result  that  the  organic  and  the  inorganic 
worlds  have  been  drawn  nearer  together.  The  further  fact  that 
living  matter  is  composed  largely  of  four  common  chemical 
elements,  carbon,  hydrogen,  oxygen,  and  nitrogen,  and  yields  on 
analysis  no  peculiar  or  mystical  substance  or  element,  tended  to 
show  that  life  itself  might  be  merely  a  property  of  various  chemical 
elements  in  peculiar  combination. 

No  less  surprising  than  the  revelation  of  the  chemical  similarity 


392  A  SHORT  HISTORY  OF  SCIENCE 

of  living  and  lifeless  matter  was  that  by  spectrum  analysis  of  the 
chemical  composition  of  the  stars,  in  which  various  elements 
common  on  the  earth  were  readily  detected.  This  astounding 
result,  taken  together  with  the  clearer  and  more  convincing  ideas 
of  the  conservation  of  matter  and  energy,  and  of  the  similarity 
in  nature  of  heat,  light,  and  sound  as  undulations,  served  to 
demonstrate  and  to  emphasize  the  scope  and  immanence  of 
natural  law,  as  well  as  the  fine  adjustment,  balance,  and  economy 
of  nature,  and  to  cause  interference  or  governance  by  anything 
supernatural  to  seem  gratuitous  and  unwarranted. 

TREVIRANUS'  BIOLOGY  AND  LAMARCK'S  ZOOLOGICAL  PHI- 
LOSOPHY. —  Very  early  in  the  nineteenth  century  the  two  works 
here  mentioned  and  already  referred  to  appeared,  the  former 
introducing  into  science  for  the  first  time  the  word  biology, 
and  thereby  formally  recognizing  a  world  of  life  in  contradistinc- 
tion to  a  world  of  lifelessness.  Both  works  virtually  ignored  the 
old  cosmogony  as  applied  to  plants  and  animals,  and  both  sought 
after  some  new  and  less  supernatural  theory.  Lamarck  in  par- 
ticular was  bold  enough  to  suggest  that  the  elongated  neck  of 
the  giraffe  was  not  specially  created,  but  had  been  gradually 
developed  by  constant  effort  to  obtain  food  beyond  its  ordi- 
nary reach.  Both  authors  deserve  special  mention  because  with 
them  biology  began  consciously  and  frankly  to  part  company 
with  the  older  cosmogony.  Lamarck,  for  example,  after  frankly 
accepting  the  possibility  of  spontaneous  generation  for  the  origin 
of  living  matter  sought  to  explain  its  present  variety  and  differ- 
entiation by  four  laws,  which  may  be  stated  as  follows :  — 

1.  Life  naturally  tends  to  increase  and  enlarge  up  to  a  certain 
self-determined  limit. 

2.  New  organs  arise  in  response  to  new  and  reiterated  wants 
and  to  the  changes  produced  by  these  wants  or  by  efforts  to  meet 
them. 

3.  The  development  of  organs  and  their  functions  is  determined  by 
the  use  of  such  organs. 

4.  All  changes  in  organization  are  conserved  by  generation  and 
transmitted  to  offspring. 


NATURAL  SCIENCE  IN  THE  NINETEENTH  CENTURY     393 

.  .To  these  ideas  Lamarck  clung  in  spite  of  criticism,  for  in  the 
Introduction  to  his  Natural  History  of  Invertebrates,  a  much  later 
work  than  his  Zoological  Philosophy,  he  again  affirms :  — 

I  conceive  that  a  gasteropod  mollusk  [e.g.  a  snail],  which,  as  it 
crawls  along,  finds  the  need  of  touching  the  bodies  in  front  of  it, 
makes  efforts  to  touch  those  bodies  with  some  of  the  foremost  parts 
of  its  head,  and  sends  to  these  every  time  quantities  of  nervous  fluids 
as  well  as  other  liquids.  I  conceive,  I  say,  that  it  must  result  from  this 
reiterated  afflux  towards  the  points  in  question  that  the  nerves  which 
abut  at  these  points  will  by  slow  degrees  be  extended.  Now,  as  in 
the  same  circumstances,  other  fluids  of  the  animal  flow  also  to  the 
same  places,  and  especially  nourishing  fluids,  it  must  follow  that 
two  or  more  tentacles  will  appear  and  develop  insensibly  in  those 
circumstances  at  the  points  referred  to. 

The  principal  significance  of  these  views  to-day  is  in  the  attempt 
which  they  embody  to  explain  on  natural  principles  phenomena 
then  explained  only  as  supernatural. 

VOYAGES  AND  EXPLORATIONS  OF  NATURALISTS.  —  In  the  nine- 
teenth century  voyages,  expeditions,  and  explorations  for  the  first 
time  were  undertaken  for  the  sole  and  specific  purpose  of  the 
improvement  of  natural  knowledge  (to  use  a  phrase  associated  with 
the  origin  of  the  Royal  Society).  Of  these  the  first  were  those  of 
Alexander  von  Humboldt  who,  beginning  in  1799,  made  numerous 
and  extensive  journeys  and  observations  by  land  and  sea  which 
enabled  him  many  years  later  to  publish  his  monumental  Kosmos, 
a  work  replete  with  observations  and  reflections  on  natural  phi- 
losophy and  natural  history,  which  eventually  gave  him  a  place,  in 
this  century,  among  the  learned  men  of  Germany  second  only  to 
that  occupied  by  Goethe. 

In  1801,  Robert  Brown,  a  British  botanist,  worthy  of  remem- 
brance also  in  connection  with  the  so-called  Brownian  movement 
of  particles  under  the  microscope,  accompanied  an  expedition 
to  Australia  and  brought  back  representatives  of  some  4000  new 
species  of  plants.  Most  fruitful  of  all  was  Darwin's  famous  voy- 
age of  the  Beagle  to  the  Pacific  (1831-1836),  while  in  1838 
Karl  Ernst  von  Baer,  the  eminent  founder  of  comparative  embry- 


394  A  SHORT  HISTORY  OF  SCIENCE 

ology,  accompanied  an  exploring  expedition  to  Nova  Zembla; 
Dana  sailed  to  the  Pacific  in  1838-1842 ;  Huxley  in  the  Rattle- 
snake in  1846-1850;  and  Alfred  Russel  Wallace  visited  the 
Malay  Archipelago  a  little  later. 

The  result  of  these  scientific  explorations  was  to  throw  a  flood 
of  new  light  upon  the  infinite  wealth,  variety,  creative  resources 
and  capacity  of  this  earth  and  its  inhabitants,  plants  as  well  as 
animals,  and  to  reveal  adaptations  of  organisms  to  climate,  soil, 
and  other  environmental  conditions  countless  in  number  and 
marvellous  in  character,  all  of  which  raised  again  the  ancient  and 
vexing  questions :  How  did  these  adaptations  arise  ?  And  what 
was  the  origin  of  species  ? 

DARWIN'S  ORIGIN  OP  SPECIES  (1859). — For  this,  the  most 
influential  scientific  work  of  the  nineteenth  century,  and  one  of 
the  most  important  ever  written,  the  way  had  now  been  prepared 
by  the  publications  of  Malthus,  Treviranus,  Lamarck,  Lyell,  and 
Chambers.  In  particular,  as  Huxley  pointed  out,  Lyell' s  work, 
by  showing  that  the  earth  is  very  old  and  has  been  long  ages  in  the 
making  had,  since  1830,  shaken  the  confidence  of  men  of  science  in 
the  old  cosmogony  and  so  paved  the  way  for  Darwin ;  and  when  in 
1854  remains  of  prehistoric  man  were  found  with  those  of  extinct 
animals,  such  as  the  cave  bear  and  the  cave  lion,  even  popular 
confidence  in  the  Mosaic  theory  began  to  be  undermined. 

Darwin's  great  work  appeared  in  1859  and  aroused  world-wide 
criticism  and  controversy.  In  his  autobiography  Darwin  acknowl- 
edges his  constant  obligation  to  Lyell  and  also  to  Malthus, 
whose  emphasis  on  the  struggle  for  food  revealed  to  Darwin 
the  fuller  meaning  of  what  in  the  Origin  he  termed  the  struggle 
for  existence,  a  struggle  in  which  by  natural  selection  there 
must  be  progressively  a  survival  of  the  fittest.  In  the  long 
and  fierce  battle  which  now  broke  out  between  the  defenders 
of  the  old  cosmogony  and  the  new,  and  which  at  first  went 
no  further  than  proposing  to  account  for  the  origin  of  species  of 
living  things  by  natural  selection  instead  of  by  special  creation, 
Darwin  was  ably  supported  by  his  friends  the  naturalists,  —  Hux- 
ley, Hooker,  and  Lyell  in  England  and  Asa  Gray  in  America. 


NATURAL  SCIENCE  IN  THE  NINETEENTH  CENTURY     395 

Darwin's  principle  of  natural  selection  is  stated  in  his  own 
words  as  follows :  — 

As  many  more  individuals  of  each  species  are  born  than  can  pos- 
sibly survive ;  and  as,  consequently,  there  is  a  frequently  recurring 
struggle  for  existence,  it  follows  that  any  being,  if  it  vary  however 
slightly  in  any  manner  profitable  to  itself,  under  the  complex  and 
sometimes  varying  conditions  of  life,  will  have  a  better  chance  of 
surviving,  and  thus  be  naturally  selected.  From  the  strong  principle 
of  inheritance,  any  selected  variety  will  tend  to  propagate  its  new 
and  modified  form. 

THE  DESCENT  OF  MAN.  —  The  last  refuge  of  the  defenders  of 
the  old  cosmogony  was  man  himself,  and  not  a  few,  among  whom 
was  Alfred  Russel  Wallace,  co-discoverer  with  Darwin  of  the 
principle  of  natural  selection,  refused  to  align  man  and  especially 
man's  mentality,  with  lower  animals  and  their  inferior  mental 
powers.  Here  at  least,  they  affirmed,  we  see  no  evidence  of  evo- 
lution. But  as  time  has  gone  on,  and  studies  have  been  extended 
in  craniology  and  in  psychology  it  has  become  increasingly  evi- 
dent that  there  is  little  if  any  more  difference  in  brain  weight  and 
mental  power  between  the  highest  apes  and  the  lowest  men, 
than  between  these  last  and  the  highest  men.  Meantime,  the 
doctrine  of  parsimony,  in  default  of  any  other  than  a  super- 
natural hypothesis,  naturally  awarded  the  field  to  the  Darwinian 
theory. 

DECLINE  OF  THE  THEORY  OF  SPECIAL  CREATION.  —  Darwin's 
theory  of  the  method  of  origin  of  the  various  kinds  (species)  of 
plants  and  animals  by  natural  processes  under  natural  law  soon 
became  known  as  the  theory  of  organic  evolution,  and  before  a 
score  of  years  had  passed  was  almost  universally  accepted  among 
naturalists. 

It  is  the  supreme  merit  of  Darwin  to  have  thus  pointed  out  a 
method  by  which  a  process  of  gradual  development,  or  evolution, 
—  already  accepted  for  language,  art,  music,  and  (after  1830)  for 
the  earth's  crust,  and  many  years  before  urged  by  Laplace  for  the 
solar  system,  —  could  be  made  no  less  applicable  to,  and  accept- 
able for,  plants  and  animals,  and  especially  for  man.  Until  this 


396  A  SHORT  HISTORY  OF  SCIENCE 

was  done,  there  could  be  no  place  for  the  new  cosmogony  in  the 
general  mind. 

The  theory  of  organic  evolution  by  natural  selection  as  main- 
tained by  Darwin  was  naturally  subjected  forthwith  to  the  severest 
scrutiny,  and  some  of  its  details  have  been  successfully  and 
destructively  criticised.  In  particular,  his  explanation  of  the 
mechanism  of  heredity  appears  to  be  untenable,  as  does  also  his 
theory  that  small  but  incessant  variations  are  gradually  accumu- 
lated into  departures  from  the  original,  ultimately  sufficient  to 
amount  to  new  species.  The  studies  of  Mendel  and  of  Weis- 
mann  upon  inheritance  and  of  De  Vries  and  others  upon  varia- 
tion, have  supplemented  and  to  some  extent  supplanted  much  of 
Darwin's  work  upon  those  subjects.  But  apart  from  these  and 
other  readjustments  of  details,  the  Darwinian  theory  stands 
secure  and  at  present  affords  the  most  reasonable  explanation 
hitherto  proposed  of  the  origin  of  man  and  other  animals  and  of 
plants;  an  explanation,  moreover,  in  harmony  with  the  general 
law  of  evolution  now  accepted  for  the  origin  of  existing  forms  of 
language,  literature,  and  art;  of  chemical  compounds;  of  the 
earth ;  of  the  solar  system ;  and  of  the  stars.  The  law  of  evolu- 
tion, long  ago  foreshadowed  by  the  Greeks,  is  clearly  the  law  of 
the  lifeless  world,  and  there  seems  to  be  no  reason  why  it  should 
not  be  equally  applicable  to  the  world  of  life, —  including  man. 

INFLUENCE  OF  AN  AGE  OF  INVENTION  AND  INDUSTRY.  —  Ac- 
ceptance of  the  theory  of  evolution  was  quickened  by  an  increase 
in  popular  intelligence  and  a  general  openmindedness  due  in  part 
to  the  broadening  of  education,  in  part  to  the  ease  of  travel,  and 
in  part  to  the  appearance,  one  after  another,  of  revolutionary  inven- 
tions, such  as  the  steam  engine  and  cotton  machinery  with  the 
factory  system  at  the  end  of  the  eighteenth  century,  and  the  loco- 
motive, the  steamboat,  the  telegraph,  the  sewing  machine,  the 
friction  match,  and  many  more,  in  the  first  half  of  the  nineteenth 
century.  All  these  marvels  had  been  wrought  within  the  brief 
space  of  a  single  century,  while  improved  printing-presses,  cheaper 
paper,  cheaper  newspapers,  cheaper  books,  and  cheaper  illustra- 
tions, as  well  as  more  and  better  schools  and  schooling  had  con- 


NATURAL  SCIENCE  IN  THE  NINETEENTH  CENTURY     397 

tributed  immensely  to  popular  education,  mental  receptivity, 
closer  contact,  industrial  cooperation  and  general  intelligence. 

SCIENCE  IN  THE  DAWN  OF  THE  TWENTIETH  CENTURY.  —  At  the 
beginning  of  the  nineteenth  century,  science  as  such  had  no  exist- 
ence either  as  a  branch  of  learning  or  as  a  special  discipline,  — 
still  less  as  a  preparation  for  practical  life.  Mathematics,  highly 
esteemed  largely  because  of  its  ancient  origin  and  associations, 
and  natural  philosophy,  had  a  limited  recognition ;  but  the  term 
science  meant  as  yet  hardly  more  than  knowledge  or  learn- 
ing. The  eighteenth  century  had,  however,  sowed  broadcast 
the  seeds  of  science  and  the  nineteenth  soon  began  to  reap 
the  harvest.  Before  1850  scientific  schools  as  distinct  from 
others  had  been  founded  both  within  and  without  the  older 
colleges  and  universities.  New  associations  and  academies  for 
the  advancement  or  promotion  of  science  soon  sprang  up; 
science  courses  appeared  in  some  of  the  public  schools;  funds 
for  scientific  research  began  to  be  provided;  and  thousands 
of  eager  and  enthusiastic  students  began  to  prefer  science,  and 
especially  applied  science,  to  the  older  "classical"  learning. 
Meantime,  the  marvellous  achievements  of  invention  and  of  in- 
dustry had  caught  and  fixed  public  interest  and  attention,  so 
that  by  the  opening  of  the  twentieth  century,  no  branch  of  learn- 
ing stood  in  higher  favor  than  science,  either  for  its  own  sake  or 
as  a  preparation  for  useful  service  in  contemporary  life. 

The  master  keys  of  science,  now  everywhere  employed  for 
unlocking  the  problems  of  the  cosmos,  are:  first,  the  principles 
of  mathematics,  which  admit  mankind  into  the  mysteries  of  the 
relations  of  number  and  space  —  the  abstract  skeleton  of  science, 
—  and  second,  the  principles  of  evolution  and  of  energy,  which 
reveal  some,  at  least,  of  the  secrets  of  form  and  of  function, 
not  only  of  the  earth  and  of  plants  and  animals,  but  of  the 
heavens  ;  something  of  the  prodigious  forces  of  the  universe 
and  their  orderly  behavior  ;  something  of  that  apparently  in- 
finite and  eternal  energy  which,  while  forever  changing,  is  never 
lost ;  something,  though  as  yet  but  little,  of  the  nature  and  the 
processes  of  life. 


398  A  SHORT  HISTORY  OF  SCIENCE 

REFERENCES  FOR  READING 

AGASSIZ,  L.    Life  of,  by  E.  C.  Agassiz. 
CHAMBERS.     Vestiges  of  Creation. 
CLERKE.     Modern  Cosmogonies. 

DARWIN.     Origin  of  Species.    Descent  of  Man.     Voyage  of  the  Beagle. 
DARWIN,  F.     Life  of  Charles  Darwin. 
DE  VRIES.     Studies  in  the  Theory  of  Descent. 
FOSTER.     Lectures  on  the  History  of  Physiology. 
*>»HALE.    Stellar  Evolution. 

HUMBOLDT,   VON.      KosmoS.         • 

HUXLEY,  L.     Life  and  Letters  of  T.  H.  Huxley. 

HUXLEY,  T.  H.    Man's  Place  in  Nature.    Essays.    Advance  of  Science  in 

the  Last  Half  Century. 
JUDD.     The  Coming  of  Evolution. 
LAMARCK.     Zoological  Philosophy. 
LOCY.     Biology  and  Its  Makers. 
LYELL.     Principles  of  Geology.    Antiquity  of  Man. 

-  OSBORN.     From  the  Greeks  to  Darwin. 
RADOT.    Life  of  Pasteur. 

SCOTT.     The  Theory  of  Evolution. 
THOMSON.    Heredity  and  Evolution. 

-  TYLOR.    Anthropology.    Primitive  Culture. 
WALLACE.    Darwinism. 

WEISMANN.    Essays.    Evolution  Theory. 


APPENDICES 

A.    THE  OATH  OF  HIPPOCRATES  (About  400  B.C.) 

[This,  as  Gomperz  observes,  is  a  monument  in  the  history  of  civilization.  It 
is  no  less  a  monument  in  the  history  of  science,  since  it  proceeds  from  the  Father 
of  Medicine  more  than  two  thousand  years  ago  and,  if  we  except  mathematicst 
medicine  is  the  oldest  of  the  sciences.  There  are  many  translations  of  the 
"Oath,"  some  more  literal  and  some,  like  the  following,  more  free.] 

I  swear  by  Apollo  the  physician  [Healer],  and  ^Esculapius,  and  Health 
[Hygeia],  and  All-heal  [Panaceia],  and  all  the  gods  and  goddesses,  that 
according  to  my  ability  and  judgment  I  will  keep  this  oath  and  stip- 
ulation :  to  reckon  him  who  taught  me  this  art  equally  dear  to  me  as 
my  parents,  to  share  my  substance  with  him  and  relieve  his  necessities 
if  required ;  to  regard  his  offspring  as  on  the  same  footing  with  my 
own  brothers,  and  to  teach  them  this  art  if  they  should  wish  to  learn 
it,  without  fee  or  stipulation,  and  that  by  precept,  lecture  and  every 
other  mode  of  instruction,  I  will  impart  a  knowledge  of  the  art  to  my 
own  sons,  and  to  those  of  my  teachers,  and  to  disciples  bound  by  a 
stipulation  and  oath,  according  to  the  law  of  medicine,  but  to  none 
others. 

I  will  follow  that  method  of  treatment  which  according  to  my 
ability  and  judgment  I  consider  for  the  benefit  of  my  patients,  and 
abstain  from  whatever  is  deleterious  and  mischievous.  I  will  give 
no  deadly  medicine  to  anyone  if  asked,  nor  suggest  any  such  counsel; 
furthermore,  I  will  not  give  to  a  woman  an  instrument  to  produce 
abortion. 

With  purity  and  with  holiness  I  will  pass  my  life  and  practice  my 
art.  I  will  not  cut  a  person  who  is  suffering  with  a  stone,  but  will 
leave  this  to  be  done  by  practitioners  of  this  work.  Into  whatever 
houses  I  enter  I  will  go  into  them  for  the  benefit  of  the  sick,  and  will 
abstain  from  every  voluntary  act  of  mischief  and  corruption;  and 
further  from  the  seduction  of  females  or  males,  bond  or  free, 

399 


400  A  SHORT  HISTORY  OF  SCIENCE 

Whatever,  in  connection  with  my  professional  practice  or  not  in 
connection  with  it,  I  may  see  or  hear  in  the  lives  of  men,  which  ought 
not  to  be  spoken  abroad,  I  will  not  divulge,  as  reckoning  that  all  such 
should  be  kept  secret. 

While  I  continue  to  keep  this  oath  unviolated,  may  it  be  granted 
to  me  to  enjoy  life  and  the  practice  of  the  art,  respected  by  all  men  at 
all  times ;  but  should  I  trespass  and  violate  this  oath,  may  the  reverse 
be  my  lot. 

B.    THE  OPUS  MAJUS  OF  ROGER  BACON  (1267  A.D.) 
[AN  ANALYSIS  OF  THE  SIXTH  PART.    BY  J.  H.  BRIDGES.] 

Of  all  the  parts  of  the  Opus  Majus,  the  sixth  is  the  most  important.  It  treats 
of  experimental  science,  domina  omnium  scientiarum  et  finis  totius  specula- 
tionis.  Without  experience,  as  Bacon  constantly  repeats,  nothing  can  be  known 
with  certainty.  Even  the  conclusions  of  mathematical  physics,  reached  by  argu- 
ment from  certain  principles,  must  be  verified,  before  the  mind  can  rest  satisfied. 
To  this  great  science  all  the  others  are  subsidiary;  they  are  to  it  ancillae  or  hand- 
maids, an  expression  that  curiously  reminds  one  of  Francis  Bacon.  The  reason- 
ing in  favour  of  experience  is  well  worth  quoting  at  length :  — 

"  There  are  two  modes  in  which  we  acquire  knowledge,  argument  and  experi- 
ment. Argument  shuts  up  the  question,  and  makes  us  shut  it  up  too;  but  it  gives 
no  proof,  nor  does  it  remove  doubt  and  cause  the  mind  to  rest  in  the  conscious 
possession  of  truth,  unless  the  truth  is  discovered  by  way  of  experience,  e.g.  if  any 
man  who  had  never  seen  fire  were  to  prove  by  satisfactory  argument  that  fire  burns 
and  destroys  things,  the  hearer's  mind  would  not  rest  satisfied,  nor  would  he  avoid 
fire;  until  by  putting  his  hand  or  some  combustible  thing  into  it,  he  proved  by 
actual  experiment  what  the  argument  laid  down;  but  after  the  experiment  had  been 
made,  his  mind  receives  certainty  and  rests  in  the  possession  of  truth,  which  could 
not  be  given  by  argument  but  only  by  experience.  And  this  is  the  case  even  in 
mathematics,  where  there  is  the  strongest  demonstration.  For  let  any  one  have  the 
dearest  demonstration  about  an  equilateral  triangle  without  experience  of  it,  his 
mind  will  never  lay  hold  of  the  problem  until  he  has  actually  before  him  the  inter- 
secting circles  and  the  lines  drawn  from  the  point  of  section  to  the  extremities  of  a 
straight  line.  He  will  then  accept  the  conclusion  with  all  satisfaction."  (Op. 
Maj.,  p.  445  [ed.  Bridges,  ii.  167}.) 

This  important  passage,  it  seems  to  me,  marks  a  distinct  advance  in  the  philos- 
ophy of  science.  The  science  of  that  time  proceeded  wholly  per  argumentum; 
verification  was  unknown.  Not  only,  however,  does  Bacon  recognize  the  necessity 
for  experiment,  for  observation  at  first-hand,  but  he  has  a  clear  appreciation  of  the 
true  nature  of  scientific  verification.  He  has  already  expounded  his  ideal  of 
physical  science,  the  application  of  mathematics  to  determine  the  laws  of  force 
and  to  deduce  conclusions  from  these  laws;  but  he  is  perfectly  aware  that  these 


APPENDIX  B:    ROGER  BACON  401 

general  conclusions  must  be  tested  by  comparison  with  things,  must  be  verified. 
The  function  of  experimental  science  is,  in  a  word, 


"  This  Science,"  says  Bacon,  (<has  three  great  prerogatives  in  respect  to  all 
other  sciences.  The  first  is  —  that  it  investigates  their  conclusions  by  experience. 
For  the  principles  of  the  other  sciences  may  be  known  by  experience,  but  the  con- 
clusions are  drawn  from  these  principles  by  way  of  argument.  If  they  require 
particular  and  complete  knowledge  of  those  conclusions,  the  aid  of  this  science 
must  be  called  in.  It  is  true  that  mathematics  possesses  useful  experience  with 
regard  to  its  own  problems  of  figure  and  number,  which  apply  to  all  the  sciences 
and  to  experience  itself,  for  no  science  can  be  known  without  mathematics.  But 
if  we  wish  to  have  complete  and  thoroughly  verified  knowledge,  we  must  proceed 
by  the  methods  of  experimental  science."  (Op.  Maj.,  p.  44$  [ed.  Bridges,  ii. 
172-3].) 

As  an  example  of  his  method  Bacon  analyses  the  phenomena  of  the  rainbow  in 
a  thoroughly  scientific  manner. 

The  second  and  third  prerogatives  (though  not  of  such  importance)  may  also 
be  mentioned.  The  second  is  —  that  Experimental  Science  attains  to  a  knowledge 
of  truth  which  could  not  be  reached  by  the  special  sciences;  the  third  —  that  Ex- 
perimental Science,  using  and  combining  the  results  of  the  other  sciences,  is  able 
to  investigate  the  secret  operations  of  Nature,  to  predict  what  the  course  of  events 
will  be,  and  to  invent  instruments  or  machines  of  wonderful  power. 

—  Adamson  (quoted  by  A.  G.  Little)  . 


PART   VI.     EXPERIMENTAL   SCIENCE 
CHAPTER  I 

Having  laid  down  the  general  principles  of  wisdom  so  far  as  they 
are  found  in  language,  in  mathematics,  and  in  optics,  I  pass  to  the 
subject  of  experimental  science.  .  .  . 

When  Aristotle  speaks  of  knowledge  of  the  cause  as  a  higher  kind 
of  knowledge  than  that  gained  by  experience,  he  is  speaking  of  mere 
empiric  knowledge  of  a  fact ;  I  am  speaking  of  experimental  knowledge 
of  its  cause.  There  are  numerous  beliefs  commonly  held  in  the  ab- 
sence of  experiment,  and  wholly  false,  such  as  that  adamant  can  be 
broken  by  goats'  blood,  that  the  beaver  when  chased  throws  away 
his  testicles,  that  a  vessel  of  hot  water  freezes  more  rapidly  than  one  of 
cold,  and  so  on.  Experience  is  of  two  kinds :  (1)  that  in  which  we 
use  our  bodily  senses  aided  by  instruments,  and  by  evidence  of  trust- 
worthy witnesses ;  and  (2)  internal  experience  of  things  spiritual, 
which  comes  of  grace,  and  which  often  leads  to  knowledge  of  earthly 
things.  The  mind  stained  with  vice  is  like  a  rusty  or  uneven  mirror, 

2D 


402  A  SHORT  HISTORY  OF  SCIENCE 

in  which  things  seem  other  than  they  are.  Without  virtue  a  man 
may  repeat  words  like  a  parrot,  and  imitate  other  men's  wisdom  like 
an  ape,  and  all  to  no  purpose.  The  intellectual  effect  of  a  stainless 
life  is  well  illustrated  in  the  young  man  who  is  the  bearer  of  this  treatise. 
The  degrees  of  spiritual  experience  are  seven.  (1)  Spiritual  illumina- 
tion ;  (2)  virtue ;  (3)  the  gift  of  the  Holy  Spirit  described  by  Isaiah ; 
(4)  the  Beatitudes ;  (5)  spiritual  sensibility ;  (6)  Fruits,  such  as  the 
peace  of  God  which  passes  understanding ;  (7)  states  of  Rapture.  — 

CHAPTER  II 

It  is  solely  by  the  aid  of  this  science  that  we  shall  be  able  to  disabuse 
men  of  the  fraudulent  tricks  by  which  magicians  have  imposed  on 
them.  As  compared  with  other  sciences,  this  science  has  three  char- 
acteristics (" prerogatives").  Of  these  the  first  is,  that  it  constitutes 
a  test  to  which  all  the  conclusions  of  other  sciences  are  to  be  subjected. 
In  other  sciences  the  principles  are  discovered  by  experiment,  but  the 
conclusion  by  reasoning.  An  instance  of  this  is  afforded  by  the  rain- 
bow, and  by  other  phenomena  of  a  similar  kind,  as  haloes,  etc.  The 
natural  philosopher  forms  a  judgment  on  these  things :  the  experi- 
menter proceeds  to  test  the  judgment.  He  seeks  for  visible  objects 
in  which  the  colours  of  the  rainbow  appear  in  the  same  order.  He 
finds  this  the  case  with  Irish  hexagonal  crystals  when  held  in  the  sun's 
rays.  This  property,  he  discovers,  is  not  peculiar  to  these  crystals, 
but  is  common  to  all  transparent  substances  of  similar  shape,  simi- 
larly placed.  He  finds  these  colours  again  on  the  surface  of  crystals 
when  slightly  roughened.  He  finds  them  in  the  drops  that  fall  from 
the  rower's  oar,  when  the  sun's  rays  strike  them,  or  from  a  water- 
wheel,  or  in  the  morning-dew  on  the  grass.  They  may  be  seen  again 
in  sunshine  when  the  eye  is  half  opened,  and  in  many  other  cases. 

CHAPTER  III 

The  shape  in  which  the  colours  are  disposed  will  vary.  Sometimes 
it  is  rectangular,  sometimes  circular. 

CHAPTER  IV 

Armed  with  these  terrestrial  facts,  the  experimenter  proceeds  to 
examine  the  celestial  phenomenon.  He  finds,  on  examining  the 
sun's  altitude  and  that  of  the  summit  of  the  bow,  that  the  two  vary 
inversely.  The  bow  is  always  opposite  the  sun.  A  line  may  be  drawn 


APPENDIX  B:    ROGER  BACON  403 

from  the  centre  of  the  sun  through  the  eye  of  the  observer  and  the 
centre  of  the  circle  of  which  the  bow  is  an  arc  to  the  sun's  nadir.  As 
one  extremity  of  this  line  is  depressed,  the  other  is  elevated.  It  be- 
comes thus  possible  to  compute  the  altitude  of  the  sun  beyond  which 
no  rainbow  is  possible,  and  also  the  maximum  altitude  of  the  bow. 
It  will  be  found  both  by  calculation  and  experience  that  this  altitude 
in  the  latitude  of  Paris  is  forty- two  degrees. 

CHAPTER  V 

Still  further  investigating  the  shape  of  the  iris,  and  the  portion  of  it 
that  can  be  seen,  the  experimenter  conceives  a  cone  of  which  the 
apex  is  the  eye,  the  base  is  the  circle  of  the  iris,  the  axis  being  the  line 
already  described  drawn  from  the  sun's  centre  through  the  eye  to  the 
sun's  nadir.  In  cases  where  this  cone  is  very  short,  the  whole  of  the 
base  may  be  above  the  horizon,  as  may  often  be  seen  in  the  spray  of 
a  waterfall.  In  the  sky,  however,  the  cone  is  too  elongated  to  admit 
of  this :  the  base  is  bisected  in  various  proportions  by  the  plane  of 
the  horizon.  The  arcs  visible  are  not  portions  of  the  same  circle. 
When  the  sun  is  high,  and  a  small  arc  is  visible,  it  belongs  to  a  larger 
circle  than  the  arc  seen  when  the  sun  is  rising  or  setting.  A  bow  can 
be  seen  when  the  sun  is  just  below  the  horizon ;  but  owing  to  terres- 
trial vapours,  only  the  crown  of  the  arch  is  usually  seen. 

CHAPTER  VI 

In  some  latitudes  there  can  be  no  rainbow  at  noon  even  in  the  win- 
ter solstice.  When  the  latitude  (i.e.  the  distance  from  the  zenith 
to  the  equator)  is  24°  25',  the  sun's  altitude  at  noon  in  the  winter 
solstice  will  be  42°,  therefore  there  can  be  no  bow.  Passing  north 
from  this  latitude,  there  can  always  be  a  noon  rainbow  till  we  come 
to  latitude  66°  25',  when  at  the  winter  solstice  there  is  no  sun.  Similar 
calculations  can  be  made  for  other  latitudes. 

CHAPTER  VII 

We  have  now  to  inquire  whether  the  iris  comes  from  incident, 
reflected,  or  refracted  rays.  Is  the  bow  an  image  of  the  sun?  Are 
the  colours  on  the  clouds  real?  Why  is  the  iris  of  circular  form? 
Here  we  call  experiment  to  our  aid.  We  find  on  trial  that  if  we  move 
in  a  direction  parallel  to  the  rainbow  it  follows  us  with  a  velocity 
exactly  equal  to  our  own.  The  same  phenomenon  occurs  with  respect 


404  A  SHORT  HISTORY  OF  SCIENCE 

to  the  sun.  We  have  seen  that  the  sun  is  always  opposite  the  rain- 
bow; the  line  between  the  centre  of  the  bow  and  the  centre  of  the 
sun  passing  through  the  eye  of  the  observer.  If  the  sun  were  appar- 
ently stationary,  this  would  involve  the  bow  moving  much  faster  than 
the  observer,  the  latter  moving  through  the  same  angle,  but  at  less 
distance  from  the  apex.  But  this  is  not  so.  Therefore  there  is  an 
apparent  motion  of  the  sun  concurrently  with  that  of  the  bow.  The 
case  is  analogous  to  what  happens  when  a  hundred  men  are  ranged  in 
line  facing  the  sun.  Each  sees  the  sun  in  front  of  him.  Their  shadows 
seem  parallel,  though  we  know  in  reality  they  must  diverge,  yet 
owing  to  the  vast  distance  of  the  sun  this  divergence  is  imperceptible. 
We  are  thus  brought  to  the  conclusion  that,  supposing  a  rainbow  to 
occur,  each  of  the  hundred  men,  facing  backwards,  would  see  a  dif- 
ferent rainbow,  to  the  centre  of  which  his  own  shadow  would  point. 
The  rays  causing  the  iris  are  therefore  not  incident  rays,  otherwise 
the  colour  would  appear  fixed  in  the  cloud.  And  for  the  same  reason 
they  are  not  refracted  rays,  for  in  refraction  the  image  does  not  follow 
the  change  of  place  of  the  observer,  as  is  the  case  here.  One  condi- 
tion of  the  phenomenon  is  that  the  atmosphere  shall  be  more  illumi- 
nated at  the  standpoint  of  the  observer,  and  less  at  the  position  of  the 
cloud.  The  movement  of  the  sun  from  east  to  west  during  the 
appearance  of  the  rainbow  may  be  left  out  of  account. 

CHAPTER  VIII 

The  colours  in  the  bow  arise  from  an  ocular  deception.  They  are 
analogous  to  those  which  appear  when  the  eyes  are  weak  or  half -shut. 
They  are  not  due  to  the  same  cause  as  the  colours  produced  when 
light  shines  through  a  crystal,  since  these  do  not,  like  the  colours 
of  the  rainbow,  shift  with  the  position  of  the  observer. 

CHAPTER  IX 

Each  drop  of  rain  in  the  cloud  is  to  be  regarded  as  a  spherical  mirror ; 
these  being  small  and  close  together,  the  effect  is  that  of  a  continuous 
image  rather  than  of  a  multitude  of  images.  The  colour  is  due  to 
the  distortion  of  the  image  caused  by  the  sphericity  of  the  mirror. 

CHAPTER  X 

The  diversity  of  colours  has  been  attributed  to  varieties  in  the 
texture  of  the  cloud,  the  denser  parts  producing  violet  and  blue,  the 


APPENDIX  B:    ROGER  BACON  405 

lighter  parts  red  and  orange.  But  we  see  the  same  colours  in  the 
dew  drops,  where  there  can  be  no  such  differences  of  density ;  simi- 
larly in  the  crystal.  Aristotle  has  been  wrongly  translated  and 
interpreted  in  this  matter.  Another  erroneous  belief  is  that  lunar 
rainbows  occur  only  once  in  fifty  years.  They  may  occur  at  any  full 
moon  under  suitable  atmospheric  conditions. 

CHAPTER  XI 

The  shape  of  the  bow  is  a  difficulty.  It  cannot  be  explained  by 
refraction.  It  is  to  be  observed  that  the  same  colour  is  continued  all 
round  the  circle  in  each  ring.  All  parts  of  the  ring  therefore  preserve 
the  same  relation  of  the  solar  ray  to  the  eye.  This  implies  circularity 
of  form.  It  is  asked  why  the  whole  space  contained  by  the  circle  is 
not  occupied  with  colour.  Because  from  the  points  in  this  central 
area  rays  equal  to  the  angle  of  incidence  are  not  reflected  to  the  eye. 

CHAPTER  XII 

The  cloud  therefore  is  not  coloured ;  the  appearance  of  colour,  for 
it  is  only  an  appearance,  is  given  by  rays  reflected  from  the  raindrops. 
Of  colours  there  are  five,  white,  blue,  red,  green,  black ;  though  Aris- 
totle, dividing  blue  and  green  into  other  shades,  speaks  of  seven. 
These  colours  appear  to  have  some  relation  to  the  various  structures 
of  the  eye.  In  addition  to  the  problem  of  the  rainbow,  there  is  the 
problem  of  haloes  and  coronal.  On  this  I  give  the  best  explanation 
that  as  yet  occurs  to  me.  I  do  not  however,  pretend  that  it  is  satis- 
factory. Far  more  careful  experiments,  made  with  properly  con- 
structed instruments,  are  needed  before  an  adequate  explanation 
can  be  given. 

THE   SECOND   PREROGATIVE   OF   EXPERIMENTAL   SCIENCE 

In  all  sciences  Experiment  is  able  to  reveal  truths  quite  unconnected 
with  the  discussion  of  principles,  and  with  regard  to  which  it  is  useless 
in  the  first  instance  to  assign  a  reason.  The  initial  state  of  mind 
should  be  readiness  to  believe ;  this  should  be  followed  by  experiment : 
reasoning  should  come  last.  I  subjoin  examples  of  my  meaning. 

1.  The  astronomer  constructs  his  spherical  astrolabe,  by  which  he 
can  observe  the  precise  longitude  and  latitude  of  heavenly  bodies 
at  different  times.  But  it  is  not  inconceivable  that  experiment  may 
devise  means  of  bringing  this  instrument  into  such  relation  with  the 


406  A  SHORT  HISTORY  OF  SCIENCE 

revolution  of  the  heavens  that  it  should  follow  their  course.  The 
motion  of  the  tides,  the  periodic  changes  in  certain  diseases,  the 
diurnal  opening  and  closing  of  flowers,  are  facts  tending  to  belief 
that  such  a  discovery  is  possible.  If  effected  it  would  supersede  all 
other  astronomical  instruments.  2.  My  next  example  relates  to  the 
act  of  prolonging  human  life.  As  yet  we  have  nothing  to  rely  on  but 
ordinary  rules  of  health.  These  are  observed  but  by  few,  and  usually 
not  till  the  close  of  life,  when  it  is  too  late.  If  a  suitable  regimen 
were  observed  by  all,  no  doubt  life  would  be  much  prolonged.  But 
there  are  special  remedies  unknown  as  yet  to  medicine,  but  to  be  found 
by  experiment,  which  may  extend  the  period  of  life  much  further. 
Observation  of  the  habits  of  certain  animals  may  guide  us  to  truths 
in  this  matter  which  are  as  yet  hidden.  Other  indications  are  given 
in  the  works  of  Aristotle,  Pliny,  Artephius,  and  others.  A  combina- 
tion of  gold,  pearl,  flower  of  sea-dew,  spermaceti,  aloes,  bone  of  stag's 
heart,  flesh  of  Tyrian  snake  and  of  ^Ethiopian  dragon,  properly  pre- 
pared in  due  proportions,  might  promote  longevity  to  an  extent 
hitherto  unimagined. 

3.  A  third  example  may  be  found  in  Alchemy.  The  problem  here 
is  not  merely  to  transmute  the  baser  into  the  more  precious  metals, 
but  to  promote  gold  to  its  highest  degree  of  perfection.  In  this  per- 
fected gold  we  should  probably  have  a  further  aid  to  the  prolongation 
of  life. 

THIRD   PREROGATIVE   OF   EXPERIMENTAL  SCIENCE 

In  this  we  leave  altogether  the  domain  of  the  sciences  now  recog- 
nized, and  open  out  entirely  new  departments  of  research.  At  present 
the  influences  exerted  on  us  by  the  stars  can  only  be  known  through 
difficult  astronomical  calculations.  Experimental  science  may  enable 
us  to  estimate  them  directly.  It  may  be  possible  for  us  to  act  on  the 
character  of  the  inhabitants  of  any  region  by  altering  their  environ- 
ment. Inventions  of  the  greatest  utility  may  be  discovered,  as 
perpetual  fire,  or  explosive  substances,  or  modes  of  counteracting 
dangerous  poisons,  and  innumerable  other  properties  of  matter  as 
yet  unknown  for  want  of  experiment.  The  Magnet,  of  which  use  is 
already  made,  is  but  a  type  of  other  mutual  attractions  exerted  by 
bodies  at  a  distance.  For  instance,  if  a  young  sapling  be  longitudinally 
divided  and  the  two  divisions  be  brought  near  together,  held  each  by 
the  middle,  the  extremities  will  bend  towards  each  other.  In  conclu- 


APPENDIX  C:    COPERNICUS  407 

sion,  I  may  point  out  the  influence  which  the  possessors  of  this  science 
may  exercise  in  the  promotion  of  Christianity  among  the  heathen, 
whether  in  subduing  their  pride,  in  disabusing  them  of  false  beliefs 
in  magic,  or  in  overcoming  their  material  force. 


C.    DEDICATION  OF 

THE  REVOLUTIONS  OF   THE  HEAVENLY  BODIES 
BY  NICOLAUS-  COPERNICUS   (1543) 

To  POPE  PAUL  III 

I  can  easily  conceive,  most  Holy  Father,  that  as  soon  as  some 
people  learn  that  in  this  book  which  I  have  written  concerning  the 
revolutions  of  the  heavenly  bodies,  I  ascribe  certain  motions  to  the 
Earth,  they  will  cry  out  at  once  that  I  and  my  theory  should  be  re- 
jected. For  I  am  not  so  much  in  love  with  my  conclusions  as  not  to 
weigh  what  others  will  think  about  them,  and  although  I  know  that 
the  meditations  of  a  philosopher  are  far  removed  from  the  judgment 
of  the  laity,  because  his  endeavor  is  to  seek  out  the  truth  in  all  things, 
so  far  as  this  is  permitted  by  God  to  the  human  reason,  I  still  believe 
that  one  must  avoid  theories  altogether  foreign  to  orthodoxy.  Ac- 
cordingly, when  I  considered  in  my  own  mind  how  absurd  a  perform- 
ance it  must  seem  to  those  who  know  that  the  judgment  of  many 
centuries  has  approved  the  view  that  the  Earth  remains  fixed  as  centre 
in  the  midst  of  the  heavens,  if  I  should  on  the  contrary,  assert  that  the 
Earth  moves ;  I  was  for  a  long  time  at  a  loss  to  know  whether  I  should 
publish  the  commentaries  which  I  have  written  in  proof  of  its  motion, 
or  whether  it  were  not  better  to  follow  the  example  of  the  Pythag- 
oreans and  of  some  others,  who  were  accustomed  to  transmit  the 
secrets  of  philosophy  not  in  writing  but  orally,  and  only  to  their  rela- 
tives and  friends,  as  the  letter  from  Lysis  to  Hipparchus  bears  wit- 
ness. They  did  this,  it  seems  to  me,  not  as  some  think,  because  of  a 
certain  selfish  reluctance  to  give  their  views  to  the  world,  but  in 
order  that  the  noblest  truths,  worked  out  by  the  careful  study  of  great 
men,  should  not  be  despised  by  those  who  are  vexed  at  the  idea  of 
taking  great  pains  with  any  form  of  literature  except  such  as  would 
be  profitable,  or  by  those  who,  if  they  are  driven  to  the  study  of  phi- 
losophy for  its  own  sake  by  the  admonitions  and  the  example  of  others, 
nevertheless,  on  account  of  their  stupidity,  hold  a  place  among  philoso- 


408  A  SHORT  HISTORY  OF  SCIENCE 

phers  similar  to  that  of  drones  among  bees.  Therefore,  when  I  con- 
sidered this  carefully,  the  contempt  which  I  had  to  fear  because  of 
the  novelty  and  apparent  absurdity  of  my  view,  nearly  induced  me  to- 
abandon  utterly  the  work  I  had  begun. 

My  friends,  however,  in  spite  of  long  delay  and  even  resistance  on 
my  part,  withheld  me  from  this  decision.  First  among  these  was 
Nicolaus  Schonberg,  Cardinal  of  Capua,  distinguished  in  all  branches 
of  learning.  Next  to  him  comes  my  very  dear  friend,  Tidemann 
Giese,  Bishop  of  Culm,  a  most  earnest  student,  as  he  is,  of  sacred  and, 
indeed,  of  all  good  learning.  The  latter  has  often  urged  me,  at  times 
even  spurring  me  on  with  reproaches,  to  publish  and  at  last  bring  to 
light  the  book  which  had  lain  in  my  study  not  nine  years  merely,  but 
already  going  on  four  times  nine.  Not  a  few  other  very  eminent  and 
scholarly  men  made  the  same  request,  urging  that  I  should  no  longer 
through  fear  refuse  to  give  out  my  work  for  the  common  benefit  of 
students  of  Mathematics.  They  said  I  should  find  that  the  more 
absurd  most  men  now  thought  this  theory  of  mine  concerning  the 
motion  of  the  Earth,  the  more  admiration  and  gratitude  it  would  com- 
mand after  they  saw  in  the  publication  of  my  commentaries,  the  mist 
of  absurdity  cleared  away  by  most  transparent  proofs.  So,  influenced 
by  these  advisers  and  this  hope,  I  have  at  length  allowed  my  friends 
to  publish  the  work,  as  they  had  long  besought  me  to  do. 

But  perhaps  your  Holiness  will  not  so  much  wonder  that  I  have 
ventured  to  publish  these  studies  of  mine,  after  having  taken  such 
pains  in  elaborating  them  that  I  have  not  hesitated  to  commit  to 
writing  my  views  of  the  motion  of  the  Earth,  as  you  will  be  curious  to 
hear  how  it  occurred  to  me  to  venture,  contrary  to  the  accepted  view 
of  mathematicians,  and  well-nigh  contrary  to  common  sense,  to  form 
a  conception  of  any  terrestial  motion  whatsoever.  Therefore  I  would 
not  have  it  unknown  to  Your  Holiness,  that  the  only  thing  which 
induced  me  to  look  for  another  way  of  reckoning  the  movements  of 
the  heavenly  bodies  was  that  I  knew  that  mathematicians  by  no  means 
agree  in  their  investigations  thereof.  For,  in  the  first  place,  they  are 
so  much  in  doubt  concerning  the  motion  of  the  sun  and  the  moon, 
that  they  cannot  even  demonstrate  and  prove  by  observation  the 
constant  length  of  a  complete  year ;  and  in  the  second  place,  in  deter- 
mining the  motions  both  of  these  and  of  the  other  five  planets,  they 
fail  to  employ  consistently  one  set  of  first  principles  and  hypotheses, 
but  use  methods  of  proof  based  only  upon  the  apparent  revolutions 


APPENDIX  C:   COPERNICUS  409 

and  motions.  For  some  employ  concentric  circles  only ;  others,  eccen- 
tric circles  and  epicycles ;  and  even  by  these  means  they  do  not  com- 
pletely attain  the  desired  end.  For,  although  those  who  have  de- 
pended upon  concentric  circles  have  shown  that  certain  diverse  mo- 
tions can  be  deduced  from  these,  yet  they  have  not  succeeded  thereby 
in  laying  down  any  sure  principle,  corresponding  indisputably  to  'the 
phenomena.  These,  on  the  other  hand,  who  have  devised  systems  of 
eccentric  circles,  although  they  seem  in  great  part  to  have  solved  the 
apparent  movements  by  calculations  which  by  these  eccentrics  are 
made  to  fit,  have  nevertheless  introduced  many  things  which  seem 
to  contradict  the  first  principles  of  the  uniformity  of  motion.  Nor 
have  they  been  able  to  discover  or  calculate  from  these  the  main 
point,  which  is  the  shape  of  the  world  and  the  fixed  symmetry  of  its 
parts;  but  their  procedure  has  been  as  if  someone  were  to  collect 
hands,  feet,  a  head,  and  other  members  from  various  places,  all  very 
fine  in  themselves,  but  not  proportionate  to  one  body,  and  no  single 
one  corresponding  in  its  turn  to  the  others,  so  that  a  monster  rather 
than  a  man  would  be  formed  from  them.  Thus  in  their  process  of 
demonstration  which  they  term  a  "method,"  they  are  found  to  have 
omitted  something  essential,  or  to  have  included  something  foreign 
and  not  pertaining  to  the  matter  in  hand.  This  certainly  would  never 
have  happened  to  them  if  they  had  followed  fixed  principles ;  for  if 
the  hypotheses  they  assumed  were  not  false,  all  that  resulted  there- 
from would  be  verified  indubitably.  Those  things  which  I  am  say- 
ing now  may  be  obscure,  yet  they  will  be  made  clearer  in  their  proper 
place. 

Therefore,  having  turned  over  in  my  mind  for  a  long  time  this  un- 
certainty of  the  traditional  mathematical  methods  of  calculating  the 
motions  of  the  celestial  bodies,  I  began  to  grow  disgusted  that  no 
more  consistent  scheme  of  the  movements  of  the  mechanism  of  the 
universe,  set  up  for  our  benefit  by  that  best  and  most  law-abiding 
Architect  of  all  things,  was  agreed  upon  by  philosophers  who  other- 
wise investigate  so  carefully  the  most  minute  details  of  this  world. 
Wherefore  I  undertook  the  task  of  rereading  the  books  of  all  the  phi- 
losophers I  could  get  access  to,  to  see  whether  anyone  ever  was  of  the 
opinion  that  the  motions  of  the  celestial  bodies  were  other  than  those 
postulated  by  the  men  who  taught  mathematics  in  the  schools.  And 
I  found  first,  indeed,  in  Cicero,  that  Hicetas  perceived  that  the  Earth 
moved ;  and  afterward  in  Plutarch  I  found  that  some  others  were  of 


410  A  SHORT  HISTORY  OF  SCIENCE? 

this  opinion,  whose  words  I  have  seen  fit  to  quote  here,  that  they  may 
be  accessible  to  all :  — 

Some  maintain  that  the  Earth  is  stationary,  but  Philolaus  the  Pythag- 
orean says  that  it  revolves  in  a  circle  about  the  fire  of  the  ecliptic,  like  the 
sun  and  moon.  Heraklides  of  Pontus  and  Ekphantus  the  Pythagorean  make 
the  Earth  move,  not  changing  its  position,  however,  confined  in  its  falling  and 
rising  around  its  own  centre  in  the  manner  of  a  wheel. 

Taking  this  as  a  starting-point,  I  began  to  consider  the  mobility  of 
the  Earth ;  and  although  the  idea  seemed  absurd,  yet  because  I  knew 
that  the  liberty  had  been  granted  to  others  before  me  to  postulate  all 
sorts  of  little  circles  for  explaining  the  phenomena  of  the  stars,  I 
thought  I  also  might  easily  be  permitted  to  try  whether  by  postulating 
some  motion  of  the  Earth,  more  reliable  conclusions  could  be  reached 
regarding  the  revolution  of  the  heavenly  bodies,  than  those  of  my 
predecessors. 

And  so,  after  postulating  movements,  which,  farther  on  in  the  book, 
I  ascribe  to  the  Earth,  I  have  found  by  many  and  long  observations 
that  if  the  movements  of  the  other  planets  are  assumed  for  the  circular 
motion  of  the  Earth  and  are  substituted  for  the  revolution  of  each 
star,  not  only  do  their  phenomena  follow  logically  therefrom,  but  the 
relative  positions  and  magnitudes  both  of  the  stars  and  all  their  orbits, 
and  of  the  heavens  themselves,  become  so  closely  related  that  in  none 
of  its  parts  can  anything  be  changed  without  causing  confusion  in 
the  other  parts  and  in  the  whole  universe.  Therefore,  in  the  course 
of  the  work  I  have  followed  this  plan :  I  describe  in  the  first  book  all 
the  positions  of  the  orbits  together  with  the  movements  which  I 
ascribe  to  the  Earth,  in  order  that  this  book  might  contain,  as  it 
were,  the  general  scheme  of  the  universe.  Thereafter  in  the  remaining 
books,  I  set  forth  the  motions  of  the  other  stars  and  of  all  their  orbits 
together  with  the  movement  of  the  Earth,  in  order  that  one  may  see 
from  this  to  what  extent  the  movements  and  appearances  of  the 
other  stars  and  their  orbits  can  be  saved,  if  they  are  transferred  to  the 
movement  of  the  Earth.  Nor  do  I  doubt  that  ingenious  and  learned 
mathematicians  will  sustain  me,  if  they  are  willing  to  recognize  and 
weigh,  not  superficially,  but  with  that  thoroughness  which  Philosophy 
demands  above  all  things,  those  matters  which  have  been  adduced 
by  me  in  this  work  to  demonstrate  these  theories.  In  order,  how- 
ever, that  both  the  learned  and  the  unlearned  equally  may  see  that 


APPENDIX  C:    COPERNICUS  411 

I  do  not  avoid  anyone's  judgment,  I  have  preferred  to  dedicate  these 
lucubrations  of  mine  to  Your  Holiness  rather  than  to  any  other,  be- 
cause, even  in  this  remote  corner  of  the  world  where  I  live,  you  are 
considered  to  be  the  most  eminent  man  in  dignity  of  rank  and  in  love 
of  all  learning  and  even  of  mathematics,  so  that  by  your  authority 
and  judmgent  you  can  easily  suppress  the  bites  of  slanderers,  albeit 
the  proverb  hath  it  that  there  is  no  remedy  for  the  bite  of  a  sycophant. 
If  perchance  there  shall  be  idle  talkers,  who,  though  they  are  ignorant 
of  all  mathematical  sciences,  nevertheless  assume  the  right  to  pass 
judgment  on  these  things,  and  if  they  should  dare  to  criticise  and 
attack  this  theory  of  mine  because  of  some  passage  of  scripture  which 
they  have  falsely  distorted  for  their  own  purpose,  I  care  not  at  all; 
I  will  even  despise  their  judgment  as  foolish.  For  it  is  not  unknown 
that  Lactantius,  otherwise  a  famous  writer  but  a  poor  mathematician, 
speaks  most  childishly  of  the  shape  of  the  Earth  when  he  makes  fun 
of  those  who  said  that  the  Earth  has  the  form  of  a  sphere.  It  should 
not  seem  strange  then  to  zealous  students,  if  some  such  people  shall 
ridicule  us  also.  Mathematics  are  written  for  mathematicians,  to 
whom,  if  my  opinion  does  not  deceive  me,  our  labors  will  seem  to 
contribute  something  to  the  ecclesiastical  state  whose  chief  office 
Your  Holiness  now  occupies ;  for  when  not  so  very  long  ago,  under 
Leo  X,  in  the  Lateran  Council  the  question  of  revising  the  ecclesiastical 
calendar  was  discussed,  it  then  remained  unsettled,  simply  because 
the  length  of  the  years  and  the  months,  and  the  motions  of  the  sun 
and  moon  were  held  to  have  been  not  yet  sufficiently  determined. 
Since  that  time,  I  have  given  my  attention  to  observing  these  more 
accurately,  urged  on  by  a  very  distinguished  man,  Paul,  Bishop  of 
Fossombrone,  who  at  that  time  had  charge  of  the  matter.  But  what 
I  may  have  accomplished  herein  I  leave  to  the  judgment  of  Your 
Holiness  in  particular,  and  to  that  of  all  other  learned  mathematicians ; 
and  lest  I  seem  to  Your  Holiness  to  promise  more  regarding  the  use- 
fulness of  the  work  than  I  can  perform,  I  now  pass  to  the  work  itself. 
(—  From  the  Harvard  Classics,  Vol.  39,  55-30.) 


412  A  SHORT  HISTORY  OF  SCIENCE 

D.  HARVEY'S  DEDICATION  OF  HIS  WORK  ON  THE  MOTION  OF 
THE  HEART  AND  THE  CIRCULATION  OF  THE  BLOOD  (1628) 

TO  HIS  VERY  DEAR  FRIEND,  DOCTOR  ARGENT,  THE  EXCELLENT  AND  AC- 
COMPLISHED PRESIDENT  OF  THE  ROYAL  COLLEGE  OF  PHYSICIANS,  AND 
TO  OTHER  LEARNED  PHYSICIANS,  HIS  MOST  ESTEEMED  COLLEAGUES 

I  have  already  and  repeatedly  presented  you,  my  learned  friends, 
with  my  new  views  of  the  motion  and  function  of  the  heart,  in  my 
anatomical  lectures ;  but  having  now  for  more  than  nine  years  con- 
firmed these  views  by  multiplied  demonstrations  in  your  presence, 
illustrated  them  by  arguments,  and  freed  them  from  the  objections  of 
the  most  learned  and  skilful  anatomists,  I  at  length  yield  to  the  re- 
quests, I  might  say  entreaties,  of  many,  and  here  present  them  for  a 
general  consideration  in  this  treatise. 

Were  not  the  work  indeed  presented  through  you,  my  learned 
friends,  I  should  scarce  hope  that  it  could  come  out  scatheless  and 
complete;  for  you  have  in  general  been  the  faithful  witnesses  of 
almost  all  the  instances  from  which  I  have  either  collected  the  truth 
or  confuted  error.  You  have  seen  my  dissections,  and  at  my  demon- 
strations of  all  that  I  maintained  to  be  objects  of  sense,  you  have  been 
accustomed  to  stand  by  and  bear  me  out  with  your  testimony.  And 
as  this  book  alone  declares  the  blood  to  course  and  revolve  by  a  new 
route,  very  different  from  the  ancient  and  beaten  pathway  trodden 
for  so  many  ages,  and  illustrated  by  such  a  host  of  learned  and  distin- 
guished men,  I  was  greatly  afraid  lest  I  might  be  charged  with  pre- 
sumption did  I  lay  my  work  before  the  public  at  home,  or  send  it 
beyond  seas  for  impression,  unless  I  had  first  proposed  the  subject  to 
you,  had  confirmed  its  conclusions  by  ocular  demonstrations  in  your 
presence,  had  replied  to  your  doubts  and  objections,  and  secured  the 
assent  and  support  of  our  distinguished  President.  For  I  was  most 
intimately  persuaded,  that  if  I  could  make  good  my  proposition  before 
you  and  our  College,  illustrious  by  its  numerous  body  of  learned  in- 
dividuals, I  had  less  to  fear  from  others.  I  even  ventured  to  hope 
that  I  should  have  the  comfort  of  finding  all  that  you  had  granted  me 
in  your  sheer  love  of  truth,  conceded  by  others  who  were  philosophers 
like  yourselves.  True  philosophers,  who  are  only  eager  for  truth  and 
knowledge,  never  regard  themselves  as  already  so  thoroughly  informed, 
but  that  they  welcome  further  information  from  whomsoever  and  from 
wheresoever  it  may  come ;  nor  are  they  so  narrow  minded  as  to  imagine 


APPENDIX  D:  HARVEY  413 

any  of  the  arts  or  sciences  transmitted  to  us  by  the  ancients,  in  such 
a  state  of  forwardness  or  completeness,  that  nothing  is  left  for  the 
ingenuity  and  industry  of  others.  On  the  contrary,  very  many  main- 
tain that  all  we  know  is  still  infinitely  less  than  all  that  still  remains 
unknown ;  nor  do  philosophers  pin  their  faith  to  others'  precepts  in 
such  wise  that  they  lose  their  liberty,  and  cease  to  give  credence  to 
the  conclusions  of  their  proper  senses.  Neither  do  they  swear  such 
fealty  to  their  mistress  Antiquity  that  they  openly,  and  in  sight  of 
all,  deny  and  desert  their  friend  Truth.  But  even  as  they  see  that 
the  credulous  and  vain  are  disposed  at  the  first  blush  to  accept  and 
believe  everything  that  is  proposed  to  them,  so  do  they  observe  that 
the  dull  and  unintellectual  are  indisposed  to  see  what  lies  before  their 
eyes,  and  even  deny  the  light  of  the  noon-day  sun.  They  teach  us 
in  our  course  of  philosophy  to  sedulously  avoid  the  fables  of  poets 
and  the  fancies  of  the  vulgar,  as  the  false  conclusions  of  the  sceptics. 
And  then  the  studious  and  good  and  true,  never  suffer  their  minds  to 
be  warped  by  the  passions  of  hatred  and  envy,  which  unfit  men  duly 
to  weigh  the  arguments  that  are  advanced  in  behalf  of  truth,  or  to 
appreciate  the  proposition  that  is  even  fairly  demonstrated.  Neither 
do  they  think  it  unworthy  of  them  to  change  their  opinion  if  truth 
and  undoubted  demonstration  require  them  to  do  so.  They  do  not 
esteem  it  discreditable  to  desert  error,  though  sanctioned  by  the 
highest  antiquity,  for  they  know  full  well  that  to  err,  to  be  deceived, 
is  human;  that  many  things  are  discovered  by  accident  and  that 
many  may  be  learned  indifferently  from  any  quarter,  by  an  old  man 
from  a  youth,  by  a  person  of  understanding  from  one  of  inferior 
capacity. 

My  dear  colleagues,  I  had  no  purpose  to  swell  this  treatise  into  a 
large  volume  by  quoting  the  names  and  writings  of  anatomists,  or  to 
make  a  parade  of  the  strength  of  my  memory,  the  extent  of  my  read- 
ing, and  the  amount  of  my  pains ;  because  I  profess  both  to  learn  and 
to  teach  anatomy,  not  from  books  but  from  dissections ;  not  from 
the  positions  of  philosophers  but  from  the  fabric  of  nature ;  and  then 
because  I  do  not  think  it  right  or  proper  to  strive  to  take  from  the 
ancients  any  honor  that  is  their  due,  nor  yet  to  dispute  with  the 
moderns,  and  enter  into  controversy  with  those  who  have  excelled  in 
anatomy  and  been  my  teachers.  I  would  not  charge  with  wilful 
falsehood  anyone  who  was  sincerely  anxious  for  truth,  nor  lay  it  to 
anyone's  door  as  a  crime  that  he  had  fallen  into  error.  I  avow  myself 


414  A  SHORT  HISTORY  OF  SCIENCE 

the  partisan  of  truth  alone;  and  I  can  indeed  say  that  I  have  used 
all  my  endeavors,  bestowed  all  my  pains  on  an  attempt  to  produce 
something  that  should  be  agreeable  to  the  good,  profitable  to  the 
learned,  and  useful  to  letters. 

Farewell,  most  worthy  Doctors, 

And  think  kindly  of  your  Anatomist 

WILLIAM  HARVEY. 

E.    GALILEO  BEFORE  THE  INQUISITION  (1633) 
I.   His  CONDEMNATION 

We,  GASPARO  del  titolo  di  S.  Croce,  in  Gierusalemme  Borgia; 

FRA  FELICE  CENTINO  del  titolo  di  S.  Anastasia,  detto  d'Ascoli ; 

Guroo  del  titolo  di  S.  Maria  del  Popolo  Bentivoglio ; 

FRA  DESIDERIO  SCAGLIA  del  titolo  di  S.  Carlo,  detto  di  Cremona; 

FRA  ANTONIO  BARBERINO,  detto  di  S.  Onofrio ; 

LAUDIVIO  ZACCHIA  del  titolo  di  S.  Pietro  in  Vincolo,  detto  di  S.  Sisto; 

BERLINGERO  del  titolo  di  S.  Agostino,  Gessi; 

FABRICIO  del  titolo  di  S.  Lorenzo  in  pane  e  perna,  Verospi,  chiamato 
Prete; 

FRANCESCO  di  S.  Lorenzo,  in  Damaso  Barberino ;   e 

MARTINO  di  S.  Maria  Nuova,  Ginetti  Diaconi ; 

by  the  Grace  of  God,  Cardinals  of  the  Holy  Roman  Church,  Inquisi- 
tors-General throughout  the  whole  Christian  Republic,  Special  Depu- 
ties of  the  Holy  Apostolical  Chair  against  heretical  depravity, 

Whereas  you,  Galileo,  son  of  the  late  Vincenzo  Galilei  of  Florence, 
aged  seventy  years,  were  denounced  in  1615  to  this  Holy  Office,  for 
holding  as  true  the  false  doctrine  taught  by  inany,  namely,  that  the 
sun  is  immovable  in  the  centre  of  the  world,  and  that  the  earth 
moves,  and  also  with  a  diurnal  motion ;  also  for  having  pupils  whom 
you  instructed  in  the  same  opinions;  also  for  maintaining  a  corre- 
spondence on  the  same  with  some  German  mathematicians ;  also  for 
publishing  certain  letters  on  the  solar  spots,  in  which  you  developed 
the  same  doctrine  as  truth;  also  for  answering  the  objections  which 
were  continually  produced  from  the  Holy  Scriptures,  by  glozing  the 
said  Scriptures  according  to  your  own  meaning ;  and  whereas  there- 
upon was  produced  the  copy  of  a  writing,  in  form  of  a  letter,  confessedly 
written  by  you  to  a  person  formerly  your  pupil,  in  which,  following 
the  hypotheses  of  Copernicus,  you  include  several  propositions  con- 
trary to  the  true  sense  and  authority  of  the  Holy  Scripture : 


APPENDIX  E:    GALILEO  415 

Therefore  this  holy  tribunal  being  desirous  of  providing  against 
the  disorder  and  mischief  thence  proceeding  and  increasing  to  the 
detriment  of  the  holy  faith,  by  the  desire  of  His  Holiness,  and  of  the 
Most  Eminent  Lords  Cardinals  of  this  supreme  and  universal  Inqui- 
sition, the  two  propositions  of  the  stability  of  the  sun,  and  the  motion 
of  the  earth,  were  qualified  by  the  Theological  Qualifiers  as  follows  : 

The  proposition  that  the  sun  is  the  centre  of  the  world  and  im- 
movable from  its  place  is  absurd,  philosophically  false,  and  formally 
heretical,  because  it  is  expressly  contrary  to  the  Holy  Scripture. 

The  proposition  that  the  earth  is  not  the  centre  of  the  world,  nor 
immovable,  but  that  it  moves,  and  also  with  a  diurnal  motion,  is  also 
absurd,  philosophically  false,  and,  theologically  considered,  at  least 
erroneous  in  faith. 

But  whereas  being  pleased  at  that  time  to  deal  mildly  with  you, 
it  was  decreed  in  the  Holy  Congregation,  held  before  His  Holiness  on 
the  25th  day  of  February,  1616,  that  His  Eminence,  the  Lord  Cardinal 
Bellarmine,  should  enjoin  you  to  give  up  altogether  the  said  false 
doctrine;  if  you  should  refuse,  that  you  should  be  ordered  by  the 
Commissary  of  the  Holy  Office  to  relinquish  it,  not  to  teach  it  to  others, 
not  to  defend  it,  nor  ever  mention  it,  and  in  default  of  acquiescence 
that  you  should  be  imprisoned;  and  in  execution  of  this  decree,  on 
the  following  day  at  the  palace,  in  presence  of  His  Eminence  the  said 
Lord  Cardinal  Bellarmine,  after  you  had  been  mildly  admonished  by 
the  said  Lord  Cardinal,  you  were  commanded  by  the  acting  Com- 
missary of  the  Holy  Office,  before  a  notary  and  witnesses  to  relinquish 
altogether  the  said  false  opinion,  and  in  future  neither  to  defend  nor 
teach  it  in  any  manner,  neither  verbally  nor  in  writing,  and  upon 
your  promising  obedience,  you  were  dismissed. 

And  in  order  that  so  pernicious  a  doctrine  might  be  altogether 
rooted  out,  nor  insinuate  itself  further  to  the  heavy  detriment  of  the 
Catholic  faith,  a  decree  emanated  from  the  Holy  Congregation  of  the 
Index  prohibiting  the  books  which  treat  of  this  doctrine ;  and  it  was 
declared  false  and  altogether  contrary  to  the  Holy  and  Divine  Scripture. 

And  whereas  a  book  has  since  appeared,  published  at  Florence 
last  year,  the  title  of  which  showed  that  you  were  the  author,  which 
is :  The  Dialogue  of  Galileo  Galilei,  on  the  Two  Principal  Systems  of 
the  World,  the  Ptolemaic  and  Copernican;  and  whereas  the  Holy 
Congregation  has  heard  that,  in  consequence  of  the  printing  of  the 
said  book,  the  false  opinion  of  the  earth's  motion  and  stability  of  the 


416  A  SHORT  HISTORY  OF  SCIENCE 

sun  is  daily  gaining  ground ;  the  said  book  has  been  taken  into  careful 
consideration,  and  in  it  has  been  detected  a  glaring  violation  of  the 
said  order,  which  had  been  intimated  to  you;  inasmuch  as  in  this 
book  you  have  defended  the  said  opinion,  already  in  ^our  presence 
condemned ;  although  in  the  said  book  you  labor  with  many  circum- 
locutions to  produce  the  belief  that  it  is  left  by  you  undecided,  and 
in  express  terms  probable ;  which  is  equally  a  very  grave  error,  since 
an  opinion  can  in  no  way  be  probable  which  has  been  already  declared 
and  finally  determined  contrary  to  the  Divine  Scripture : 

Therefore  by  our  order  you  were  cited  to  this  Holy  Office,  where, 
on  your  examination  upon  oath,  you  acknowledged  the  said  book  as 
written  and  printed  by  you.  You  also  confessed  that  you  began  to 
write  the  said  book  ten  or  twelve  years  ago,  after  the  order  aforesaid 
had  been  given;  also,  that  you  demanded  licence  to  publish  it,  but 
without  signifying  to  those  who  granted  you  this  permission  that  you 
had  been  commanded  not  to  hold,  defend  or  teach  the  said  doctrine 
in  any  manner. 

You  also  confessed  that  the  style  of  the  said  book  was,  in  many 
places,  so  composed  that  the  reader  might  think  the  arguments 
adduced  on  the  false  side  to  be  so  worded  as  more  effectually  to  en- 
tangle the  understanding  than  to  be  easily  solved,  alleging  in  excuse, 
that  you  have  thus  run  into  an  error,  foreign  (as  you  say)  to  your  in- 
tention, from  writing  in  the  form  of  a  dialogue,  and  in  consequence 
of  the  natural  complacency  which  everyone  feels  in  regard  to  his  own 
subtilities,  and  in  showing  himself  more  skilful  than  the  generality  of 
mankind  in  contriving,  even  in  favor  of  false  propositions,  ingenious 
and  apparently  probable  arguments. 

And,  upon  a  convenient  time  having  been  given  to  you  for  making 
your  defense,  you  produced  a  certificate  in  the  handwriting  of  His 
Eminence  the  Lord  Cardinal  Bellarmine,  procured  as  you  said,  by 
yourself,  that  you  might  defend  yourself  against  the  calumnies  of 
your  enemies,  who  reported  that  you  had  abjured  your  opinions,  and 
had  been  punished  by  the  Holy  Office;  in  which  certificate  it  is 
declared  that  you  had  not  abjured,  nor  had  been  punished,  but  merely 
that  the  declaration  made  by  His  Holiness,  and  promulgated  by  the 
Holy  Congregation  of  the  Index,  had  been  announced  to  you,  which 
declares  that  the  opinion  of  the  motion  of  the  earth,  and  the  stability 
of  the  sun,  is  contrary  to  the  Holy  Scriptures,  and,  therefore,  cannot 
be  held  or  defended.  Wherefore,  since  no  mention  is  there  made  of 


APPENDIX  E:  GALILEO  417 

two  articles  of  the  order,  to  wit,  the  order  "not  to  teach,"  and  "in 
any  manner/'  you  argued  that  we  ought  to  believe  that,  in  the  lapse 
of  fourteen  or  sixteen  years,  they  had  escaped  your  memory,  and 
that  this  was  also  the  reason  why  you  were  so  silent  as  to  the  order, 
when  you  sought  permission  to  publish  your  book,  and  that  this  is 
said  by  you  not  to  excuse  your  error,  but  that  it  may  be  attributed 
to  vainglorious  ambition,  rather  than  to  malice.  But  this  very  cer- 
tificate, produced  on  your  behalf,  has  greatly  aggravated  your  offense, 
since  it  is  therein  declared  that  the  said  opinion  is  contrary  to  the 
Holy  Scripture ;  and  yet  you  have  dared  to  treat  of  it,  to  defend  it, 
and  to  argue  that  it  is  probable ;  nor  is  there  any  extenuation  in  the 
licence  artfully  and  cunningly  extorted  by  you,  since  you  did  not 
intimate  the  command  imposed  upon  you. 

But  whereas  it  appeared  to  us  that  you  had  not  disclosed  the  whole 
truth  in  regard  to  your  intentions,  We  thought  it  necessary  to  pro- 
ceed to  the  rigorous  examination  of  you,  in  which  (without  any  preju- 
dice to  what  you  had  confessed,  and  which  is  above  detailed  against 
you,  with  regard  to  your  said  intention)  you  answered  like  a  good 
Catholic.  Therefore,  having  seen  and  maturely  considered  the 
merits  of  your  cause,  with  your  said  confessions  and  excuses,  and 
everything  else  which  ought  to  be  seen  and  considered,  We  have 
come  to  the  underwritten  final  sentence  against  you. 

Invoking,  therefore,  the  Most  Holy  name  of  Our  Lord  Jesus  Christ, 
and  of  His  Most  Glorious  Virgin  Mother  Mary,  by  this  our  final 
sentence,  which,  sitting  in  council  and  judgment  for  the  tribunal  of 
the  Reverend  Masters  of  Sacred  Theology,  and  Doctors  of  Both 
Laws,  Our  Assessors,  We  put  forth  in  this  writing  touching  the  matters 
and  controversies  before  us,  between  the  Magnificent  Charles  Sin- 
cerus,  Doctor  of  Both  Laws,  Fiscal  Proctor  of  this  Holy  Office,  of  the 
one  part,  and  you,  Galileo  Galilei,  an  examined  and  confessed  criminal 
from  this  present  writing  as  above,  of  the  other  part.  We  pronounce, 
judge  and  declare,  that  you,  the  said  Galileo,  by  reason  of  these  things 
which  have  been  detailed  in  the  course  of  this  writing,  and  which,  as 
above,  you  have  confessed,  have  rendered  yourself  vehemently  sus- 
pected by  this  Holy  Office  of  heresy ;  that  is  to  say,  that  you  believe 
and  hold  the  false  doctrine,  and  contrary  to  the  Holy  and  Divine 
Scriptures,  namely,  that  the  sun  is  the  centre  of  the  world,  and  that 
it  does  not  move  from  the  east  to  west,  that  the  earth  does  move 
and  is  not  the  centre  of  the  world ;  also  that  an  opinion  can  be  held 
2E 


418  A  SHORT  HISTORY  OF  SCIENCE 

and  supported  as  probable  after  it  has  been  declared  and  finally  de- 
creed contrary  to  the  Holy  Scripture,  and  consequently  that  you  have 
incurred  all  the  censures  and  penalties  enjoined  and  promulgated  in 
the  sacred  canons,  and  other  general  and  particular  constitutions, 
against  delinquents  of  this  description.^  From  which  it  is  Our  pleas- 
ure that  you  be  absolved,  provided  that,  first,  with  a  sincere  heart 
and  unfeigned  faith,  in  Our  presence,  you  abjure,  curse,  and  detest 
the  said  errors  and  heresies  and  every  other  error  and  heresy  contrary 
to  the  Catholic  and  Apostolic  Church  of  Rome,  in  the  form  now  shown 
to  you. 

But,  that  your  grievous  and  pernicious  error  and  transgression  may 
not  go  altogether  unpunished,  and  that  you  may  be  made  more  cautious 
in  the  future,  and  may  be  a  warning  to  others  to  abstain  from  delin- 
quencies of  this  sort,  We  decree  that  the  book  of  the  Dialogues  of 
Galileo  Galilei  be  prohibited  by  a  public  edict. 

We  condemn  you  to  the  formal  prison  of  this  Holy  Office  for  a 
period  determinable  at  Our  pleasure ;  and  by  way  of  salutary  penance, 
We  order  you,  during  the  next  three  years,  to  recite  once  a  week  the 
seven  Penitential  Psalms. 

Reserving  to  ourselves  the  power  of  moderating,  commuting,  or 
taking  off  the  whole  or  part  of  the  said  punishment  or  penance. 

And  so  We  say,  pronounce,  and  by  Our  sentence  declare,  decree, 
and  reserve,  in  this  and  every  other  better  form  and  manner,  which 
lawfully  we  may  and  can  use. 

So  we,  the  undersigned  Cardinals,  pronounce. 

FELICE,  Cardinal  di  Ascoli, 
GUIDO,  Cardinal  Bentivoglio, 
DESIDERIO,  Cardinal  di  Cremona? 
ANTONIO,  Cardinal  S.  Onofrio, 
BERLINGERO,  Cardinal  Gessi, 
FABRICIO,  Cardinal  Verospi, 
MARTINO,  Cardinal  Ginetti. 

II.   His  RECANTATION 

I  Galileo  Galilei,  son  of  the  late  Vincenzo  Galilei  of  Florence,  aged 
seventy  years,  being  brought  personally  to  judgment,  and  kneeling 
before  you,  Most  Eminent  and  Most  Reverend  Lords  Cardinals, 
General  Inquisitors  of  the  Universal  Christian  Republic  against  heret- 


APPENDIX  E:  GALILEO  419 

ical  depravity,  having  before  my  eyes  the  Holy  Gospels,  which  I 
touch  with  my  own  hands,  swear,  that  I  have  always  believed,  and 
now  believe,  and  with  the  help  of  God  will  in  future  believe,  every 
article  which  the  Holy  Catholic  and  Apostolic  Church  of  Rome  holds, 
teaches  and  preaches.  But  because  I  had  been  enjoined  by  this  Holy 
Office  altogether  to  abandon  the  false  opinion  which  maintains  that 
the  sun  is  the  centre  and  immovable,  and  forbidden  to  hold,  defend, 
or  teach  the  said  false  doctrine  in  any  manner,  and  after  it  had  been 
signified  to  me  that  the  said  doctrine  is  repugnant  with  the  Holy 
Scripture,  I  have  written  and  printed  a  book,  in  which  I  treat  of 
the  same  doctrine  now  condemned,  and  adduce  reasons  with  great 
force  in  support  of  the  same,  without  giving  any  solution,  and 
therefore,  have  been  judged  grievously  suspected  of  heresy;  that 
is  to  say,  that  I  have  held  and  believed  that  the  sun  is  the  centre 
of  the  world  and  immovable,  and  that  the  earth  is  not  the  centre  and 
movable. 

Wishing,  therefore,  to  remove  from  the  mind  of  Your  Emi- 
nences, and  of  every  Catholic  Christian,  this  vehement  suspicion 
rightfully  entertained  towards  me,  with  a  sincere  heart  and  un- 
feigned faith,  I  abjure,  curse  and  detest  the  said  errors  and  here- 
sies, and  generally  every  other  error  and  sect  contrary  to  the  said 
Holy  Church;  and  I  swear  that  I  will  nevermore  in  future  say 
or  assert  anything  verbally,  or  in  writing,  which  may  give  rise 
to  a  similar  suspicion  of  me;  but  if  I  shall  know  any  heretic, 
or  anyone  suspected  of  heresy,  that  I  will  denounce  him  to  this 
Holy  Office,  or  to  the  Inquisitor  and  Ordinary  of  the  place  in  which 
I  may  be. 

I  swear,  moreover,  and  promise,  that  I  will  fulfill,  and  observe 
fully,  all  the  penances  which  have  been  or  shall  be  laid  to  me  by  this 
Holy  Office.  But  if  it  shall  happen  that  I  violate  any  of  my  said 
promises,  oaths  and  protestations  (which  God  avert!),  I  subject 
myself  to  all  the  pains  and  punishments  which  have  been  de- 
creed and  promulgated  by  the  sacred  canons,  and  other  general 
and  particular  constitutions,  against  delinquents  of  this  description. 
So  may  God  help  me,  and  His  Holy  Gospels,  which  I  touch  with  my 
own  hands. 

I,  the  above-named  Galileo  Galilei,  have  abjured,  sworn,  promised 
and  bound  myself,  as  above,  and  in  witness  thereof  with  my  own  hand 
have  subscribed  this  present  writing  of  my  abjuration,  which  I  have 


420  A  SHORT  HISTORY  OF  SCIENCE 

recited  word  for  word.     At  Rome  in  the  Convent  of  Minerva,  22nd 
June,  1633. 

I,  Galileo  Galilei,  have  abjured  as  above  with  my  own  hand. 

—  From  ROUTLEDGE.    History  of  Science.    See  also  K.  VON  GEBLER. 
Galileo  Galilei  and  the  Roman  Curia.     London,  1879. 

F.    PREFACE  TO  THE 
PHILOSOPHIC  NATURALIS  PRINCIPIA  MATHEMATICA    (1686) 

BY  ISAAC  NEWTON 

Since  the  ancients  (as  we  are  told  by  Pappus)  made  great  account 
of  the  science  of  mechanics  in  the  investigation  of  natural  things; 
and  the  moderns,  laying  aside  substantial  forms  and  occult  qualities, 
have  endeavored  to  subject  the  phenomena  of  nature  to  the  laws  of 
mathematics,  I  have  in  this  treatise  cultivated  mathematics  so  far  as 
it  regards  philosophy.     The  ancients  considered  mechanics  in  a  two- 
fold respect;    as  rational,  which  proceeds  accurately  by  demonstra- 
tion, and  practical.     To  practical  mechanics  all  the  manual  arts  be- 
long, from  which  mechanics  took  its  name.     But  as  artificers  do  not 
work  with  perfect  accuracy,  it  comes  to  pass  that  mechanics  is  so 
distinguished  from  geometry,  that  what  is  perfectly  accurate  is  called 
geometrical;    what  is  less  so  is  called  mechanical.     But  the  errors 
are  not  in  the  art  but  in  the  artificers.     He  that  works  with  less  ac- 
curacy is  an  imperfect  mechanic  :  and  if  any  could  work  with  perfect 
accuracy,  he  would  be  the  most  perfect  mechanic  of  all;    for  the 
description  of  right  lines  and  circles,  upon  which  geometry  is  founded, 
belongs  to  mechanics.     Geometry  does  not  teach  us  to  draw  these 
lines,  but  requires  them  to  be  drawn ;  for  it  requires  that  the  learner 
should  first  be  taught  to  describe  these  accurately,  before  he  enters 
upon  geometry ;  then  it  shows  how  by  these  operations  problems  may 
be  solved.     To  describe  right  lines  and  circles  are  problems,  but  not 
geometrical  problems.     The  solution  of  these  problems  is  required 
from  mechanics ;   and  by  geometry  the  use  of  them,  when  so  solved, 
is  shown ;  and  it  is  the  glory  of  geometry  that  from  those  few  principles, 
fetched  from  without,  it  is  able  to  produce  so  many  things.     There- 
fore geometry  is  founded  in  mechanical  practice  and  is  nothing  but 
that  part  of  universal   mechanics  which  accurately  proposes  and 
demonstrates  the  art  of  measuring.     But  since  the  manual  arts  are 


APPENDIX  F:  NEWTON  421 

chiefly  conversant  in  the  moving  of  bodies,  it  comes  to  pass  that 
geometry  is  commonly  referred  to  their  magnitudes,  and  mechanics 
to  their  motion.  In  this  sense  rational  mechanics  will  be  the  science 
of  motions  resulting  from  any  forces  whatsoever,  and  of  the  forces 
required  to  produce  any  motion,  accurately  proposed  and  demon- 
strated. This  part  of  mechanics  was  cultivated  by  the  ancients  in 
the  five  powers  which  relate  to  manual  arts,  who  considered  gravity 
(it  not  being  a  manual  power)  no  otherwise  than  as  it  moved  weights 
by  those  powers.  Our  design,  not  respecting  arts,  but  philosophy, 
and  our  subject,  not  manual,  but  natural,  powers,  we  consider  chiefly 
those  things  which  relate  to  gravity,  levity,  elastic  force,  the  resistance 
of  fluids,  and  the  like  forces,  whether  attractive  or  impulsive ;  and 
therefore  we  offer  this  work  as  mathematical  principles  of  philosophy ; 
for  all  the  difficulty  of  philosophy  seems  to  consist  in  this  —  from  the 
phenomena  of  motions  to  investigate  the  forces  of  nature,  and  then 
from  these  forces  to  demonstrate  the  other  phenomena ;  and  to  this 
end  the  general  propositions  in  the  first  and  second  book  are  directed. 
In  the  third  book  we  give  an  example  of  this  in  the  explication  of  the 
system  of  the  World ;  for  by  the  propositions  mathematically  demon- 
strated in  the  first  book,  we  there  derive  from  the  celestial  phenomena 
the  forces  of  gravity  with  which  bodies  tend  to  the  sun  and  the  several 
planets.  Then,  from  these  forces,  by  other  propositions  which  are 
also  mathematical,  we  deduce  the  motions  of  the  planets,  the  comets, 
the  moon,  and  the  sea.  I  wish  we  could  derive  the  rest  of  the  phe- 
nomena of  nature  by  the  same  kind  of  reasoning  from  mechanical 
principles ;  for  I  am  induced  by  many  reasons  to  suspect  that  they 
may  all  depend  upon  certain  forces  by  which  the  particles  of  bodies, 
by  some  causes  hitherto  unknown,  are  either  mutually  impelled 
towards  each  other,  and  cohere  in  regular  figures,  or  are  repelled  and 
recede  from  each  other;  which  forces  being  unknown,  philosophers 
have  hitherto  attempted  the  search  of  nature  in  vain;  but  I  hope 
the  principles  here  laid  down  will  afford  some  light  either  to  that  or 
some  truer  method  of  philosophy. 

In  the  publication  of  this  work,  the  most  acute  and  universally 
learned  Mr.  Edmund  Halley  not  only  assisted  me  with  his  pains  in 
correcting  the  press  and  taking  care  of  the  schemes,  but  it  was  to  his 
solicitations  that  its  becoming  public  is  owing ;  for  when  he  had  ob- 
tained of  me  my  demonstrations  of  the  figures  of  the  celestial  orbits, 
he  continually  pressed  me  to  communicate  the  same  to  the  Royal 


422  A  SHORT  HISTORY  OF  SCIENCE 

Society,  who  afterwards,  by  their  kind  encouragement  and  entreaties, 
engaged  me  to  think  of  publishing  them.  But  after  I  had  begun  to 
consider  the  inequalities  of  the  lunar  motions,  and  had  entered  upon 
some  other  things  relating  to  the  laws  and  measures  of  gravity,  and 
other  forces ;  and  the  figures  that  would  be  described  by  bodies  at- 
tracted according  to  given  laws ;  and  the  motion  of  several  bodies 
moving  among  themselves ;  the  motion  of  bodies  in  resisting  mediums ; 
the  forces,  densities,  and  motions  of  mediums;  the  orbits  of  the 
comets,  and  such  like ;  I  put  off  that  publication  until  I  had  made  a 
search  into  those  matters,  and  could  put  out  the  whole  together. 
What  relates  to  the  lunar  motions  (being  imperfect)  I  have  put  all 
together  in  the  corollaries  of  proposition  66,  to  avoid  being  obliged 
to  propose  and  distinctly  demonstrate  the  several  things  there  con- 
tained in  a  method  more  prolix  than  the  subject  deserved,  and  in- 
terrupt the  series  of  the  several  propositions.  Some  things,  found  out 
after  the  rest,  I  chose  to  insert  in  places  less  suitable,  rather  than 
change  the  number  of  the  propositions  and  the  citations.  I  heartily 
beg  that  what  I  have  here  done  may  be  read  with  candor ;  and  that 
the  defects  I  have  been  guilty  of  upon  this  difficult  subject  may  be 
not  so  much  reprehended  as  kindly  supplied,  and  investigated  by  new 
endeavors  of  my  readers. 

ISAAC  NEWTON. 
CAMBRIDGE,  Trinity  College, 
May  8,  1686. 

(—  Translation  by  Andrew  Motte.  The  Harvard  Classics,  Vol.  39,  pp.  157-159.) 

G.  AN  INQUIRY  INTO  THE  CAUSES  AND  EFFECTS  OF  THE 
VARIOLA  VACCINM,  A  DISEASE  DISCOVERED  IN  SOME 
OF  THE  WESTERN  COUNTIES  OF  ENGLAND,  PARTICU- 
LARLY GLOUCESTERSHIRE  AND  KNOWN  BY  THE  NAME 
OF  THE  COW  POX 

BY  EDWARD  JENNER,  M.D.,  F.R.S.,  etc. 

[The  first  successful  attempt  —  and  this  wholly  empirical  —  to  control  smallpox 
in  the  human  subject  was  the  art  of  Inoculation  with  the  virus  of  smallpox  itself, 
a  procedure  derived  from  the  East,  and  introduced  about  1720  into  Europe  and 
America.  In  1796  Jenner  laid  the  foundation  of  experimental  medicine,  immu- 
nology and  serology,  by  his  work  on  Vaccination,  i.e.,  inoculation  with  cow-pox, 
in  a  paper  bearing  the  above  title.  The  first  edition  was  published  in  1798  and 
the  second,  from  which  the  following  extracts  are  taken,  in  1800.] 


APPENDIX  G  :   JENNER  423 

The  deviation  of  Man  from  the  state  in  which  he  was  originally 
placed  by  Nature  seems  to  have  proved  to  him  a  prolific  source  of 
Disease.  From  the  love  of  splendour,  from  the  indulgences  of  luxury, 
and  from  his  fondness  for  amusement,  he  has  familiarised  himself  with 
a  great  number  of  animals,  which  may  not  originally  have  been  in- 
tended for  his  associates.  The  Wolf,  disarmed  of  ferocity,  is  now 
pillowed  in  the  lady's  lap.  The  Cat,  the  little  Tyger  of  our  island, 
whose  natural  home  is  the  forest,  is  equally  domesticated  and  caressed. 
The  Cow,  the  Hog,  the  Sheep,  and  the  Horse,  are  all,  for  a  variety  of 
purposes,  brought  under  his  care  and  dominion. 

There  is  a  disease  to  which  the  Horse,  from  his  state  of  domestica- 
tion, is  frequently  subject.  The  Farriers  have  termed  it  the  Grease. 
It  is  an  inflammation  and  swelling  of  the  heel,  from  which  issues 
matter  possessing  properties  of  a  very  peculiar  kind,  which  seems 
capable  of  generating  a  disease  in  the  Human  Body  (after  it  has  under- 
gone the  modification  I  shall  presently  speak  of),  which  bears  so  strong 
a  resemblance  to  the  Small  Pox,  that  I  think  it  highly  probable  it  may 
be  the  source  of  that  disease. 

In  this  Dairy  Country  a  great  number  of  cows  are  kept,  and  the 
office  of  milking  is  performed  indiscriminately  by  men  and  maid 
servants.  One  of  the  former  having  been  appointed  to  apply  dress- 
ings to  the  heels  of  a  horse  affected  with  the  Grease,  and  not  paying 
due  attention  to  cleanliness,  incautiously  bears  his  part  in  milking  the 
cows,  with  some  particles  of  the  infectious  matter  adhering  to  his 
fingers.  When  this  is  the  case,  it  commonly  happens  that  a  disease 
is  communicated  to  the  cows,  and  from  the  cows  to  the  dairymaids, 
which  spreads  through  the  farm  until  most  of  the  cattle  and  domestics 
feel  its  unpleasant  consequences.  This  disease  has  obtained  the  name 
of  Cow  Pox.  It  appears  on  the  nipples  of  the  cows  in  the  form  of 
irregular  pustules.  At  their  first  appearance  they  are  commonly  of  a 
palish  blue,  or  rather  of  a  colour  somewhat  approaching  to  livid,  and 
are  surrounded  by  an  inflammation.  These  pustules,  unless  a  timely 
remedy  be  applied,  frequently  degenerate  into  phagedenic  ulcers, 
which  prove  extremely  troublesome.  The  animals  become  indisposed, 
and  the  secretion  of  milk  is  much  lessened.  Inflamed  spots  now  begin 
to  appear  on  different  parts  of  the  hands  of  the  domestics  employed 
in  milking,  and  sometimes  on  the  wrists,  which  quickly  run  on  to 
suppuration,  first  assuming  the  appearance  of  the  small  vesications 
produced  by  a  burn.  Most  commonly  they  appear  about  the  joints 


424  A  SHORT  HISTORY  OF  SCIENCE 

of  the  fingers  and  at  their  extremities;  but  whatever  parts  are  af- 
fected, if  the  situation  will  admit,  these  superficial  suppurations  put 
on  a  circular  form,  with  their  edges  more  elevated  than  their  center, 
and  of  a  colour  distantly  approaching  to  blue.  Absorption  takes 
place,  and  tumours  appear  in  each,  axilla.  The  system  becomes 
affected,  the  pulse  is  quickened ;  shivering,  succeeded  by  heat,  general 
lassitude  and  pains  about  the  loins  and  limbs,  with  vomiting,  come  on. 
The  head  is  painful,  and  the  patient  is  now  and  then  affected  with 
delirium.  These  symptoms,  varying  in  their  degrees  of  violence, 
generally  continue  from  one  day  to  three  or  four,  leaving  ulcerated 
sores  about  the  hands,  which,  from  the  sensibility  of  the  parts,  are 
very  troublesome,  and  commonly  heal  slowly,  frequently  becoming 
phagedenic,  like  those  from  whence  they  sprung.  The  lips,  nostrils, 
eyelids,  and  other  parts  of  the  body,  are  somtimes  affected  with  sores ; 
but  these  evidently  arise  from  their  being  heedlessly  rubbed  or 
scratched  with  the  patient's  infected  fingers.  No  eruptions  on  the 
skin  have  followed  the  decline  of  the  feverish  symptoms  in  any  in- 
stance that  has  come  under  my  inspection,  one  only  excepted,  and  in 
his  case  a  very  few  appeared  on  the  arms :  they  were  very  minute,  of 
a  vivid  red  colour,  and  soon  died  away  without  advancing  to  matura- 
tion ;  so  that  I  cannot  determine  whether  they  had  any  connection 
with  the  preceding  symptoms. 

Thus  the  disease  makes  its  progress  from  the  Horse  (as  I  conceive) 
to  the  nipple  of  the  Cow,  and  from  the  Cow  to  the  Human  Subject. 

Morbid  matter  of  various  kinds,  when  absorbed  into  the  system, 
may  produce  effects  in  some  degree  similar;  but  what  renders  the 
Cow  Pox  virus  so  extremely  singular,  is,  that  the  person  who  has 
been  thus  affected  is  forever  after  secure  from  the  infection  of  the 
Small  Pox ;  neither  exposure  to  the  variolous  effluvia,  nor  the  insertion 
of  the  matter  into  the  skin,  producing  this  distemper. 

In  support  of  so  extraordinary  a  fact,  I  shall  lay  before  my  reader 
a  great  number  of  instances  :  but  first  it  is  necessary  to  observe,  that 
pustulous  sores  frequently  appear  spontaneously  on  the  nipples  of 
the  cows,  and  instances  have  occurred,  though  very  rarely,  of  the 
hands  of  the  servants  employed  in  milking  being  affected  with  sores 
in  consequence,  and  even  of  their  feeling  an  indisposition  from  ab- 
sorption. These  pustules  are  of  a  much  milder  nature  than  those 
which  arise  from  that  contagion  which  constitutes  the  true  Cow  Pox. 
They  are  always  free  from  the  bluish  or  livid  tint  so  conspicuous  in 


APPENDIX  G:   JENNER  425 

the  pustules  in  that  disease.  No  erysipelas  attends  them,  nor  do  they 
shew  any  phagedenic  disposition  as  in  the  other  case,  but  quickly 
terminate  in  a  scab  without  creating  any  apparent  disorder  in  the 
Cow.  This  complaint  appears  at  various  seasons  of  the  year,  but 
most  commonly  in  the  spring,  when  the  Cows  are  first  taken  from 
their  winter  food  and  fed  with  grass.  It  is  very  apt  to  appear  also 
when  they  are  suckling  their  young.  But  this  disease  is  not  considered 
as  similar  in  any  respect  to  that  of  which  I  am  treating,  as  it  is  in- 
capable of  producing  any  specific  effects  on  the  human  constitution. 
However,  it  is  of  the  greatest  consequence  to  point  it  out  here,  lest 
the  want  of  discrimination  should  occasion  an  idea  of  security  from 
the  infection  of  the  Small  Pox,  which  might  prove  delusive. 

[Hereupon  follow  detailed  descriptions  of  numerous  cases  illustrating  Jenner's 
ideas.  Of  these  we  quote  only  two :  Case  I,  illustrating  Jenner's  observations  of 
immunity  to  smallpox  acquired  naturally  by  accidental  inoculation  or  vaccination 
with  cowpox  virus,  and  Case  XVII,  his  first  and  therefore  most  famous  example 
of  experimental  inoculation  (or  vaccination)  upon  the  person  of  a  boy  named  James 
Phipps.  This,  the  earliest  experiment  of  the  kind  ever  made,  occurred  on  May  14, 
1796.} 

CASE  I 

Joseph  Merret,  now  an  Under  Gardener  of  the  Earl  of  Berkeley, 
lived  as  a  servant  with  a  Farmer  near  this  place  in  the  year  1770, 
and  occasionally  assisted  in  milking  his  master's  cows.  Several 
horses  belonging  to  the  farm  began  to  have  sore  heels,  which  Merret 
frequently  attended.  The  cows  soon  became  affected  with  the  Cow 
Pox,  and  soon  after  several  sores  appeared  on  his  hands.  Swellings 
and  stiffness  in  each  axilla  followed,  and  he  was  so  much  indisposed 
for  several  days  as  to  be  incapable  of  pursuing  his  ordinary  employ- 
ment. Previously  to  the  appearance  of  the  distemper  among  the 
cows  there  was  no  fresh  cow  brought  into  the  farm,  nor  any  servant 
employed  who  was  affected  with  the  Cow  Pox. 

In  April,  1795,  a  general  inoculation  taking  place  here,  Merret  was 
inoculated  with  his  family ;  so  that  a  period  of  twenty-five  years  had 
elapsed  from  his  having  the  Cow  Pox  to  this  time.  However,  though 
the  variolous  matter  was  repeatedly  inserted  into  his  arm,  I  found  it 
impracticable  to  infect  him  with  it ;  an  efflorescence  only,  taking  on 
an  erysipelatous  look  about  the  centre,  appearing  on  the  skin  near 
the  punctured  parts.  During  the  whole  time  that  his  family  had  the 


426  A  SHORT  HISTORY  OF  SCIENCE 

• 

Small  Pox,  one  of  whom  had  it  very  full,  he  remained  in  the  house 
with  them,  but  received  no  injury  from  exposure  to  the  contagion. 

It  is  necessary  to  observe,  that  the  utmost  care  was  taken  to  as- 
certain, with  the  most  scrupulous  precision,  that  no  one  whose  case 
is  here  adduced  had  gone  through  the  Small  Pox  previous  to  these 
attempts  to  produce  that  disease.  ... 

CASE  XVII 

The  more  accurately  to  observe  the  progress  of  the  infection,  I 
selected  a  healthy  boy,  about  eight  years  old,  for  the  purpose  of  inocu- 
lation for  the  Cow  Pox.  The  matter  was  taken  from  a  sore  on  the 
hand  of  a  dairymaid  (Sarah  Nelmes),  who  was  infected  by  her  master's 
cows,  and  it  was  inserted,  on  the  14th  of  May,  1796,  into  the  arm  of 
the  boy  by  means  of  two  superficial  incisions,  barely  penetrating  the 
cutis,  each  about  half  an  inch  long. 

On  the  seventh  day  he  complained  of  uneasiness  in  the  axilla,  and 
on  the  ninth  he  becattie  a  little  chilly,  lost  his  appetite,  and  had  a 
slight  head-ache.  During  the  whole  of  this  day  he  was  perceptibly 
indisposed,  and  spent  the  night  with  some  degree  of  restlessness,  but 
on  the  day  following  he  was  perfectly  well. 

The  appearance  of  the  incisions  in  their  progress  to  a  state  of 
maturation  were  much  the  same  as  when  produced  in  a  similar  man- 
ner by  variolous  matter.  The  only  difference  which  I  perceived  was, 
in  the  state  of  the  limpid  fluid  arising  from  the  action  of  the  virus, 
which  assumed  rather  a  darker  hue,  and  in  that  of  the  efflorescence 
spreading  round  the  incisions,  which  had  more  of  an  erysipelatous 
look  than  we  commonly  perceive  when  variolous  matter  has  been 
made  use  of  in  the  same  manner ;  but  the  whole  died  away  (leaving 
on  the  inoculated  parts  scabs  and  subsequent  eschars)  without  giving 
me  or  my  patient  the  least  trouble. 

In  order  to  ascertain  whether  the  boy,  after  feeling  so  slight  an 
affection  of  the  system  from  the  Cow  Pox  virus,  was  secure  from  the 
contagion  of  the  Small  Pox,  he  was  inoculated  the  1st  of  July  follow- 
ing with  variolous  matter,  immediately  taken  from  a  pustule.  Several 
slight  punctures  and  incisions  were  made  on  both  his  arms,  and  the 
matter  was  carefully  inserted,  but  no  disease  followed.  The  same 
appearances  were  observable  on  the  arms  as  we  commonly  see  when 
a  patient  has  had  variolous  matter  applied  after  having  either  the  Cow 


APPENDIX  G :    JENNER  427 

Pox  or  the  Small  Pox.  Several  months  afterwards  he  was  again 
inoculated  with  variolous  matter,  but  no  sensible  effect  was  pro- 
duced on  the  constitution.  .  .  . 


I  shall  now  conclude  from  this  Inquiry  with  some  general  observa- 
tions on  the  subject,  and  on  some  others  which  are  interwoven 
with  it. 

Although  I  presume  it  may  be  unnecessary  to  produce  further 
testimony  in  support  of  my  assertion  "  that  the  Cow  Pox  protects  the 
human  constitution  from  the  infection  of  the  Small  Pox,"  yet  it  affords 
me  considerable  satisfaction  to  say,  that  Lord  Somerville,  the  Presi- 
dent of  the  Board  of  Agriculture,  to  whom  this  paper  was  shown  by 
Sir  Joseph  Banks,  has  found  upon  inquiry  that  the  statements  were 
confirmed  by  the  concurring  testimony  of  Mr.  Dollan,  a  surgeon, 
who  resides  in  a  dairy  country  remote  from  this,  in  which  these  ob- 
servations were  made.  With  respect  to  the  opinion  adduced  "that 
the  source  of  the  infection  is  a  peculiar  morbid  matter  arising  in  the 
horse,"  although  I  have  not  been  able  to  prove  it  from  actual  experi- 
ments conducted  immediately  under  my  own  eye,  yet  the  evidence 
I  have  adduced  appears  sufficient  to  establish  it. 

They  who  are  not  in  the  habit  of  conducting  experiments  may  not 
be  aware  of  the  coincidence  of  circumstance  necessary  for  their  being 
managed  so  as  to  prove  perfectly  decisive ;  nor  how  often  men  engaged 
in  professional  pursuits  are  liable  to  interruptions  which  disappoint 
them  almost  at  the  instant  of  their  being  accomplished.  However, 
I  feel  no  room  for  hesitation  respecting  the  common  origin  of  the 
disease,  being  well  convinced  that  it  never  appears  among  the  cows 
(except  it  can  be  traced  to  a  cow  introduced  among  the  general  herd 
which  has  been  previously  infected,  or  to  an  infected  servant)  unless 
they  have  been  milked  by  some  one  who,  at  the  same  time,  has  the 
care  of  a  horse  affected  with  diseased  heels. 

The  spring  of  the  year  1797,  which  I  intended  particularly  to  have 
devoted  to  the  completion  of  this  investigation,  proved  from  its  dry- 
ness,  remarkably  adverse  to  my  wishes ;  for  it  frequently  happens, 
while  the  farmers'  horses  are  exposed  to  the  cold  rains  which  fall  at 
that  season  that  their  heels  become  diseased,  and  no  Cow  Pox  then 
appeared  in  the  neighborhood. 

The  active  quality  of  the  virus  from  the  horses'  heels  is  greatly 


428  A  SHORT  HISTORY  OF  SCIENCE 

increased  after  it  has  acted  on  the  nipples  of  the  cow,  as  it  rarely 
happens  that  the  horse  affects  his  dresser  with  sores,  and  as  rarely  that 
a  milkmaid  escapes  the  infection  when  she  milks  infected  cows.  It 
is  most  active  at  the  commencement  of  the  disease,  even  before  it 
has  acquired  a  pus-like  appearance;  indeed  I  am  not  confident 
whether  this  property  in  the  matter  does  not  entirely  cease  as  soon 
as  it  is  secreted  in  the  form  of  pus.  I  am  induced  to  think  it  does 
cease,  and  that  it  is  the  thin  darkish-looking  fluid  only,  oozing  from 
the  newly-formed  cracks  in  the  heels,  similar  to  what  sometimes 
appears  from  erysipelatous  blisters,  which  give  the  disease.  Nor 
am  I  certain  that  the  nipples  of  the  cows  are  at  all  times  in  a  state  to 
receive  the  infection.  The  appearance  of  the  disease  in  the  spring: 
and  the  early  part  of  the  summer,  when  they  are  disposed  to  be  af- 
fected with  spontaneous  eruptions  so  much  more  frequently  than  at 
other  seasons,  induces  me  to  think,  that  the  virus  from  the  horse  must 
be  received  upon  them  when  they  are  in  this  state,  in  order  to  produce 
effects :  experiments,  however,  must  determine  these  points.  But 
it  is  clear  that  when  the  Cow  Pox  virus  is  once  generated,  that  the 
cows  cannot  resist  the  contagion,  in  whatever  state  their  nipples  may 
chance  to  be,  if  they  are  milked  with  an  infected  hand. 

Whether  the  matter,  either  from  the  cow  or  the  horse  will  affect 
the  sound  skin  of  the  human  body,  I  cannot  positively  determine ; 
probably  it  will  not,  unless  on  those  parts  where  the  cuticle  is  ex- 
tremely thin,  as  on  the  lips  for  example.  I  have  known  an  instance 
of  a  poor  girl  who  produced  an  ulceration  on  her  lip  by  frequently 
holding  her  finger  to  her  mouth  to  cool  the  raging  of  a  Cow-Pox  sore 
by  blowing  upon  it.  The  hands  of  the  farmers'  servants  here,  from 
the  nature  of  their  employments,  are  constantly  exposed  to  those 
injuries  which  occasion  abrasions  of  the  cuticle,  to  punctures  from 
thornes  and  such  like  accidents ;  so  that  they  are  always  in  a  state  to 
feel  the  consequences  of  exposure  to  infectious  matter. 

It  is  singular  to  observe  that  the  Cow  Pox  virus,  although  it  renders 
the  constitution  unsusceptible  of  the  variolous,  should,  nevertheless, 
leave  it  unchanged  with  respect  to  its  own  action.  I  have  already 
produced  an  instance  to  point  out  this,  and  shall  now  corroborate  it 
with  another. 

Elizabeth  Wynne,  who  had  the  Cow  Pox  in  the  year  1759,  was 
inoculated  with  variolous  matter,  without  effect,  in  the  year  1797, 
and  again  caught  the  Cow  Pox  in  the  year  1798.  When  I  saw  her, 


APPENDIX  G:    JENNER  429 

which  was  on  the  eighth  day  after  she  received  the  infection,  I  found 
her  affected  with  general  lassitude,  shiverings,  alternating  with  heat, 
coldness  of  the  extremities,  and  a  quick  and  irregular  pulse.  These 
symptoms  were  preceded  by  a  pain  in  the  axilla.  On  her  hand  was 
one  large  pustulous  sore. 

It  is  curious  also  to  observe,  that  the  virus,  which  with  respect  to  its 
effects  is  undetermined  and  uncertain  previously  to  it  passing  from  the 
horse  through  the  medium  of  the  cow,  should  then  not  only  become 
more  active,  but  should  invariably  and  completely  possess  those  spe- 
cific properties  which  induce  in  the  human  constitution  symptoms  sim- 
ilar to  those  of  the  variolous  fever,  and  effect  in  it  that  peculiar  change 
which  forever  renders  it  unsusceptible  of  the  variolous  contagion. 

May  it  not  then  be  reasonably  conjectured,  that  the  source  of  the 
Small  Pox  is  morbid  matter  of  a  peculiar  kind,  generated  by  a  disease 
in  the  horse,  and  that  accidental  circumstances  may  have  again  and 
again  arisen,  still  working  new  changes  upon  it,  until  it  has  ac- 
quired the  contagious  and  malignant  form  under  which  we  now  com- 
monly see  it  making  its  devastations  amongst  us?  And,  from  a 
consideration  of  the  change  which  the  infectious  matter  undergoes 
from  producing  a  disease  on  the  cow,  may  we  not  conceive  that  many 
contagious  diseases,  now  prevalent  amongst  us,  may  owe  their  present 
appearance  not  to  a  simple,  but  to  a  compound  origin  ?  For  example, 
is  it  difficult  to  imagine  that  the  measles,  the  scarlet  fever,  and  the 
ulcerous  sore  throat  with  a  spotted  skin,  have  all  sprung  from  the 
same  source,  assuming  some  variety  in  their  forms  according  to  the 
nature  of  their  new  combinations?  The  same  question  will  apply 
respecting  the  origin  of  many  other  contagious  diseases,  which  bear 
a  strong  analogy  to  each  other. 

H.  PRINCIPLES  OF  GEOLOGY :  BEING  AN  ATTEMPT  TO  EXPLAIN 
THE  FORMER  CHANGES  OF  THE  EARTH'S  SURFACE  BY 
REFERENCE  TO  CAUSES  NOW  IN  OPERATION 

BY  CHARLES  LYELL,  ESQ.,  F.R.S. 

[The  first  edition  of  this  epoch-making  work  appeared  in  1830  and  the  second 
edition,  from  which  the  following  excerpts  are  taken,  in  1832.  Few  if  any  books 
of  the  nineteenth  century  have  had  greater  influence  upon  human  thought.  The 
first  four  chapters  constitute  an  invaluable  review  of  previous  geological  opinion, 
from  the  earliest  times.  The  following  quotations  are  from  the  end  of  the 
fourth  and  the  latter  part  of  the  fifth  chapters.] 


430  A  SHORT  HISTORY  OF  SCIENCE 

We  have  now  arrived  at  the  era  of  living  authors,  and  shall  bring 
to  a  conclusion  our  sketch  of  the  progress  of  opinion  in  Geology.  .  .  . 
A  new  school  at  last  arose  who  professed  the  strictest  neutrality,  and 
the  utmost  indifference  to  the  systems  of  Werner  and  Hutton,  and 
who  were  resolved  diligently  to  devote  their  labours  to  observation. 
The  reaction,  provoked  by  the  intemperance  of  the  conflicting  par- 
ties, now  produced  a  tendency  to  extreme  caution.  Speculative 
views  were  discountenanced,  and  through  fear  of  exposing  themselves 
to  the  suspicion  of  a  bias  towards  the  dogmas  of  a  party,  some  geol- 
ogists became  anxious  to  entertain  no  opinion  whatever  on  the  causes 
of  phenomena,  and  were  inclined  to  scepticism  even  where  the  con- 
clusions deducible  from  observed  facts  scarcely  admitted  of  reasonable 
doubt. 

Geological  Society  of  London.  —  But  although  the  reluctance  to 
theorize  was  carried  somewhat  to  excess,  no  measure  could  be  more 
salutary  at  such  a  moment  than  a  suspension  of  all  attempts  to  form 
what  were  termed  "  theories  of  the  earth."  A  great  body  of  new  data 
were  required,  and  the  Geological  Society  of  London,  founded  in 
1807,  conduced  greatly  to  the  attainment  of  this  desirable  end.  To 
multiply  and  record  observations,  and  patiently  to  await  the  result 
at  some  future  period,  was  the  object  proposed  by  them,  and  it  was 
their  favourite  maxim  that  the  time  was  not  yet  come  for  a  general 
system  of  geology,  but  that  all  must  be  content  for  many  years  to  be 
exclusively  engaged  in  furnishing  materials  for  future  generalizations. 
By  acting  up  to  these  principles  with  consistency,  they  in  a  few  years 
disarmed  all  prejudice,  and  rescued  the  science  from  the  imputation 
of  being  a  dangerous,  or  at  best  but  a  visionary  pursuit. 


MODERN  PROGRESS  OF  GEOLOGY 

Study  of  Organic  Remains.  —  Inquiries  were  at  the  same  time 
prosecuted  with  great  success  by  the  French  naturalists,  who  devoted 
their  attention  especially  to  the  study  of  organic  remains.  They 
shewed  that  the  specific  characters  of  fossil  shells  and  vertebrated 
animals  might  be  determined  with  the  utmost  precision,  and  by  their 
exertions  a  degree  of  accuracy  was  introduced  into  this  department 
of  science,  of  which  it  had  never  before  been  deemed  susceptible.  It 
was  found  that,  by  the  careful  discrimination  of  the  fossil  contents  of 
strata,  the  contemporary  origin  of  different  groups  could  often  be 


APPENDIX  H:  LYELL  431 

established,  even  where  all  identity  of  mineralogical  character  was 
wanting,  and  where  no  light  could  be  derived  from  the  order  of  super- 
position. 

The  minute  investigation,  moreover,  of  the  relics  of  the  animate 
creation  of  former  ages,  had  a  powerful  effect  in  dispelling  the  illusion 
which  had  long  prevailed  concerning  the  absence  of  analogy  between 
the  ancient  and  modern  state  of  our  planet.  A  close  comparison  of 
the  recent  and  fossil  species,  and  the  inferences  drawn  in  regard  to 
their  habits,  accustomed  the  geologist  to  contemplate  the  earth  as 
having  been  at  successive  periods  the  dwelling-place  of  animals  and 
plants  of  different  races,  some  of  which  were  discovered  to  have  been 
terrestrial,  and  others  aquatic  —  some  fitted  to  live  in  seas,  others  in 
the  waters  of  lakes  and  rivers.  By  the  consideration  of  these  topics, 
the  mind  was  slowly  and  insensibly  withdrawn  from  imaginary  pic- 
tures of  catastrophes  and  chaotic  confusion,  such  as  haunted  the 
imagination  of  the  early  cosmogonists.  Numerous  proofs  were  dis- 
covered of  the  tranquil  deposition  of  sedimentary  matter  and  the 
slow  development  of  organic  life.  If  many  still  continued  to  main- 
tain, that  "  the  thread  of  induction  was  broken, "  yet  in  reasoning  by 
the  strict  rules  of  induction  from  recent  to  fossil  species,  they  vir- 
tually disclaimed  the  dogma  which  in  theory  they  professed.  The 
adoption  of  the  same  generic,  and,  in  some  cases,  even  the  same 
specific,  names  for  the  exuviae  of  fossil  animals,  and  their  living  ana- 
logues, was  an  important  step  towards  familiarising  the  mind  with  the 
idea  of  the  identity  and  unity  of  the  system  in  distant  eras.  It  was 
an  acknowledgment,  as  it  were,  that  a  considerable  part  of  the  ancient 
memorials  of  nature  were  written  in  a  living  language.  The  growing 
importance  then  of  the  natural  history  of  organic  remains,  and  its 
general  application  to  geology,  may  be  pointed  out  as  the  character- 
istic feature  of  the  progress  of  the  science  during  the  present  century. 
This  branch  of  knowledge  has  already  become  an  instrument  of  great 
power  in  the  discovery  of  truths  in  geology,  and  is  continuing  daily 
to  unfold  new  data  for  grand  and  enlarged  views  respecting  the  former 
changes  of  the  earth. 

When  we  compare  the  result  of  observations  in  the  last  thirty  years 
with  those  of  the  three  preceding  centuries,  we  cannot  but  look 
forward  with  the  most  sanguine  expectations  to  the  degree  of  excel- 
lence to  which  geology  may  be  carried,  even  by  the  labours  of  the 
present  generation.  Never,  perhaps,  did  any  science,  with  the  excep- 


432  A  SHORT  HISTORY  OF  SCIENCE 

tion  of  astronomy,  unfold,  in  an  equally  brief  period,  so  many  novel 
and  unexpected  truths,  and  overturn  so  many  preconceived  opinions. 
The  senses  had  for  ages  declared  the  earth  to  be  at  rest,  until  the 
astronomer  taught  that  it  was  carried  through  space  with  incon- 
ceivable rapidity.  In  like  manner  was  the  surface  of  this  planet 
regarded  as  having  remained  unaltered  since  its  creation,  until  the 
geologist  proved  that  it  had  been  the  theatre  of  reiterated  change, 
and  was  still  the  object  of  slow  but  never-ending  fluctuations.  The 
discovery  of  other  systems  in  the  boundless  regions  of  space  was  the 
triumph  of  astronomy  —  to  trace  the  same  system  through  various 
transformations  —  to  behold  it  at  successive  eras  adorned  with  dif- 
ferent hills  and  valleys,  lakes  and  seas,  and  peopled  with  new  inhabi- 
tants, was  the  delightful  meed  of  geological  research.  By  the  geom- 
eter were  measured  the  regions  of  space,  and  the  relative  distances 
of  the  heavenly  bodies  —  by  the  geologist  myriads  of  ages  were  reck- 
oned, not  by  arithmetical  computation,  but  by  a  train  of  physical 
events  —  a  succession  of  phenomena  in  the  animate  and  inanimate 
worlds  —  signs  which  convey  to  our  minds  more  definite  ideas  than 
figures  can  do,  of  the  immensity  of  time. 

Whether  our  investigation  of  the  earth's  history  and  structure 
will  eventually  be  productive  of  as  great  practical  benefits  to  man- 
kind, as  a  knowledge  of  the  distant  heavens,  must  remain  for  the 
decision  of  posterity.  It  was  not  till  astronomy  had  been  enriched 
by  the  observations  of  many  centuries,  and  had  made  its  way  against 
popular  prejudices  to  the  establishment  of  a  sound  theory,  that  its 
application  to  the  useful  arts  was  most  conspicuous.  The  cultiva- 
tion of  geology  began  at  a  later  period ;  and  in  every  step  which  it 
has  hitherto  made  towards  sound  ethical  principles,  it  has  had  to 
contend  against  more  violent  prepossessions.  The  practical  advan- 
tages already  derived  from  it  have  not  been  inconsiderable :  but  our 
generalizations  are  yet  imperfect,  and  they  who  follow  may  be  expected 
to  reap  the  most  valuable  fruits  of  our  labour.  Meanwhile  the  charm 
of  first  discovery  is  our  own,  and  as  we  explore  this  magnificent  field 
of  inquiry,  the  sentiment  of  a  great  historian  of  our  times  may  con- 
tinually be  present  to  our  minds,  that  ''he  who  calls  what  has  van- 
ished back  again  into  being,  enjoys  a  bliss  like  that  of  creating."  .  .  . 


APPENDIX  H:    LYELL  433 

ASSUMPTION  OF  THE  DISCORDANCE  OF  THE  ANCIENT  AND  EXISTING 
CAUSES  OF  CHANGE  UNPHILOSOPHICAL 

.  .  .  For  more  than  two  centuries  the  shelly  strata  of  the  Sub- 
Apennine  hills  afforded  matter  of  speculation  to  the  early  geologists 
of  Italy,  and  few  of  them  had  any  suspicion  that  similar  deposits 
were  then  forming  in  the  neighboring  sea.  They  were  as  unconscious 
of  the  continued  action  of  causes  still  producing  similar  effects,  as  the 
astronomers,  in  the  case  supposed  by  us,  of  the  existence  of  certain 
heavenly  bodies  still  giving  and  reflecting  light,  and  performing  their 
movements  as  in  the  olden  time.  Some  imagined  that  the  strata, 
so  rich  in  organic  remains,  instead  of  being  due  to  secondary  agents, 
had  been  so  created  in  the  beginning  of  things  by  the  fiat  of  the  Al- 
mighty ;  and  others  ascribed  the  imbedded  fossil  bodies  to  some  plastic 
power  which  resided  in  the  earth  in  the  early  ages  of  the  world.  At 
length  Donati  explored  the  bed  of  the  Adriatic,  and  found  the  closest 
resemblance  between  the  new  deposits  there  forming,  and  those 
which  constituted  hills  above  a  thousand  feet  high  in  various  parts 
of  the  peninsula.  He  ascertained  that  certain  genera  of  living  testacea 
were  grouped  together  at  the  bottom  of  the  sea  in  precisely  the  same 
manner  as  were  their  fossil  analogues  in  the  strata  of  the  hills,  and  that 
some  species  were  common  to  the  recent  and  fossil  world.  Beds  of 
shells,  moreover,  in  the  Adriatic,  were  becoming  incrusted  with  cal- 
careous rock;  and  others  were  recently  enclosed  in  deposits  of  sand 
and  clay,  precisely  as  fossil  shells  were  found  in  the  hills.  This  splen- 
did discovery  of  the  identity  of  modern  and  ancient  submarine  opera- 
tions was  not  made  without  the  aid  of  artificial  instruments,  which, 
like  the  telescope,  brought  phenomena  into  view  not  otherwise  within 
the  sphere  of  human  observation. 

In  like  manner,  in  the  Vicentin,  a  great  series  of  volcanic  and  marine 
sedimentary  rocks  were  examined  in  the  early  part  of  the  last  century ; 
but  no  geologist  suspected,  before  the  time  of  Arduino,  that  these 
were  partly  composed  of  ancient  submarine  lavas.  If,  when  these 
enquiries  were  first  made,  geologists  had  been  told  that  the  mode  of 
formation  of  such  rocks  might  be  fully  elucidated  by  the  study  of 
processes  then  going  on  in  certain  parts  of  the  Mediterranean, 
they  would  have  been  as  incredulous  as  geometers  would  have  been 
before  the  time  of  Newton,  if  any  one  had  informed  them  that, 
by  making  experiments  on  the  motion  of  bodies  on  the  earth,  they 

2F 


434  A  SHORT  HISTORY  OF  SCIENCE 

might  discover  the  laws  which  regulated  the  movements  of  distant 
planets. 

The  establishment,  from  time  to  time,  of  numerous  points  of  identi- 
fication, drew  at  length  from  geologists  a  reluctant  admission,  that 
there  was  more  correspondence  between  the  physical  constitution 
of  the  globe,  and  more  uniformity  in  the  laws  regulating  the  changes 
of  its  surface,  from  the  most  remote  eras  to  the  present,  than  they  at 
first  imagined.  If,  in  this  state  of  the  science,  they  still  despaired  or 
reconciling  every  class  of  geological  phenomena  to  the  operations  of 
ordinary  causes,  even  by  straining  analogy  to  the  utmost  limits  of 
credibility,  we  might  have  expected,  that  the  balance  of  probability 
at  least  would  now  have  been  presumed  to  incline  towards  the  identity 
of  the  causes.  But,  after  repeated  experience  of  the  failure  of  attempts 
to  speculate  on  different  classes  of  geological  phenomena,  as  belong- 
ing to  a  distinct  order  of  things,  each  new  sect  persevered  systematic- 
ally in  the  principles  adopted  by  their  predecessors.  They  invariably 
began,  as  each  new  problem  presented  itself,  whether  relating  to  the 
animate  or  inanimate  world,  to  assume  in  their  theories,  that  the 
economy  of  nature  was  formerly  governed  by  rules  quite  independent 
of  those  now  established.  Whether  they  endeavoured  to  account 
for  the  origin  of  certain  igneous  rocks,  or  to  explain  the  forces  which 
elevated  hills  or  excavated  valleys,  or  the  causes  which  led  to  the 
extinction  of  certain  races  of  animals,  they  first  presupposed  an  orig- 
inal and  dissimilar  order  of  nature ;  and  when  at  length  they  approxi- 
mated, or  entirely  came  round  to  an  opposite  opinion,  it  was  always 
with  the  feeling,  that  they  conceded  what  they  were  justified  a  priori 
in  deeming  improbable.  In  a  word,  the  same  men  who,  as  natural 
philosophers,  would  have  been  greatly  surprised  to  find  any  deviation 
from  the  usual  course  of  Nature  in  their  own  time,  were  equally  sur- 
prised, as  geologists,  not  to  find  such  deviations  at  every  period  of 
the  past. 

The  Huttonians  were  conscious  that  no  check  could  be  given  to 
the  utmost  license  of  conjecture  in  speculating  on  the  causes  of  geo- 
logical phenomena,  unless  we  can  assume  invariable  constancy  in 
the  order  of  Nature.  But  when  they  asserted  this  uniformity  with- 
out any  limitation  as  to  time,  they  were  considered,  by  the  majority 
of  their  contemporaries,  to  have  been  carried  too  far,  especially  as 
they  applied  the  same  principle  to  the  laws  of  the  organic,  as  well  as 
of  the  inanimate  world. 


APPENDIX  H:  LYELL  435 

We  shall  first  advert  briefly  to  many  difficulties  which  formerly 
appeared  insurmountable,  but  which,  in  the  last  forty  years,  have 
been  partially  or  entirely  removed  by  the  progress  of  science;  and 
shall  afterwards  consider  the  objections  that  still  remain  to  the  doc- 
trine of  absolute  uniformity. 

In  the  first  place,  it  was  necessary  for  the  supporters  of  this  doc- 
trine to  take  for  granted  incalculable  periods  of  time,  in  order  to  ex- 
plain the  formation  of  sedimentary  strata  by  causes  now  in  diurnal 
action.  The  time  which  they  required  theoretically,  is  now  granted, 
as  it  were,  or  has  become  absolutely  requisite,  to  account  for  another 
class  of  phenomena  brought  to  light  by  more  recent  investigations. 
It  must  always  have  been  evident  to  unbiassed  minds,  that  succes- 
sive strata,  containing,  in  regular  order  of  superposition,  distinct 
beds  of  shells  and  corals,  arranged  in  families  as  they  grow  at  the 
bottom  of  the  sea,  could  only  have  been  formed  by  slow  and  insen- 
sible degrees  in  a  great  lapse  of  ages,  yet,  until  organic  remains  were 
minutely  examined  and  specifically  determined,  it  was  rarely  possible 
to  prove  that  the  series  of  deposits  met  with  in  one  country  was  not 
formed  simultaneously  with  that  found  in  another.  But  we  are  now 
able  to  determine,  in  numerous  instances,  the  relative  dates  of  sedi- 
mentary rocks  in  distant  regions,  and  to  show,  by  their  organic  re- 
mains, that  they  were  not  of  contemporary  origin,  but  formed  in 
succession.  We  often  find,  that  where  an  interruption  in  the  consecu- 
tive formations  in  one  district  is  indicated  by  a  sudden  transition 
from  one  assemblage  of  fossil  species  to  another,  the  chasm  is  filled 
up,  in  some  other  district,  by  other  important  groups  of  strata. 

The  more  attentively  we  study  the  European  continent,  the  greater 
we  find  the  extension  of  the  whole  series  of  geological  formations. 
No  sooner  does  the  calendar  appear  to  be  completed,  and  the  signs 
of  a  succession  of  physical  events  arranged  in  chronological  order, 
than  we  are  called  upon  to  intercalate,  as  it  were,  some  new  periods 
of  vast  duration.  A  geologist,  whose  observations  have  been  confined 
to  England,  is  accustomed  to  consider  the  superior  and  newer  groups 
of  marine  strata  in  our  island  as  modern,  and  such  they  are,  compara- 
tively speaking;  but  when  he  has  travelled  through  the  Italian 
peninsula  and  in  Sicily,  and  has  seen  strata  of  more  recent  origin 
forming  mountains  several  thousand  feet  high,  and  has  marked  a 
long  series  both  of  volcanic  and  submarine  operations,  all  newer  than 
any  of  the  regular  strata  which  enter  largely  into  the  physical  struc- 


436  A  SHORT  HISTORY  OF  SCIENCE 

ture  of  Great  Britain,  he  returns  with  more  exalted  conceptions  of 
the  antiquity  of  some  of  our  modern  deposits,  than  he  before  enter- 
tained of  the  oldest  of  the  British  series. 

We  cannot  reflect  on  the  concessions  thus  extorted  from  us,  in 
regard  to  the  duration  of  past  time,  without  foreseeing  that  the  period 
may  arrive  when  part  of  the  Huttonian  theory  will  be  combated  on 
the  ground  of  its  departing  too  far  from  the  assumption  of  uniformity 
in  the  order  of  nature.  On  a  closer  investigation  of  extinct  volcanos, 
we  find  proofs  that  they  broke  out  at  successive  eras,  and  that  the 
eruptions  of  one  group  were  often  concluded  long  before  others  had 
commenced  their  activity.  Some  were  burning  when  one  class  of 
organic  beings  were  in  existence,  others  came  into  action  when  dif- 
ferent races  of  animals  and  plants  existed,  —  it  follows,  therefore, 
that  the  convulsions  caused  by  subterranean  movements,  which  are 
merely  another  portion  of  the  volcanic  phenomena,  occurred  also 
in  succession,  and  their  efforts  must  be  divided  into  separate  sums, 
and  assigned  to  separate  periods  of  time ;  and  this  is  not  all :  when 
we  examine  the  volcanic  products,  whether  they  be  lavas  which  flowed 
out  under  water  or  upon  dry  land,  we  find  that  intervals  of  time, 
often  of  great  length;  intervened  between  their  formation,  and  that 
the  effects  of  one  eruption  were  not  greater  in  amount  than  that 
which  now  results  during  ordinary  volcanic  convulsions.  The  ac- 
companying or  preceding  earthquakes,  therefore,  may  be  considered 
to  have  been  also  successive,  and  to  have  been  in  like  manner  inter- 
rupted by  intervals  of  time,  and  not  to  have  exceeded  in  violence 
those  now  experienced  in  the  ordinary  course  of  nature. 

Already,  therefore,  may  we  regard  the  doctrine  of  the  sudden  eleva- 
tion of  whole  continents  by  paroxysmal  eruptions  as  invalidated ;  and 
there  was  the  greatest  inconsistency  in  the  adoption  of  such  a  tenet 
by  the  Huttonians,  who  were  anxious  to  reconcile  former  changes  to 
the  present  economy  of  the  world.  It  was  contrary  to  analogy  to 
suppose  that  Nature  had  been  at  any  former  epoch  parsimonious  of 
time  and  prodigal  of  violence  —  to  imagine  that  one  district  was  not 
at  rest  while  another  was  convulsed  —  that  the  disturbing  forces  were 
not  kept  under  subjection,  so  as  never  to  carry  simultaneous  havoc 
and  desolation  over  the  whole  earth,  or  even  over  one  great  region. 
If  it  could  have  been  shown,  that  a  certain  combination  of  circum- 
stances would  at  some  future  period  produce  a  crisis  in  the  subter- 
ranean action,  we  should  certainly  have  had  no  right  to  oppose  our 


APPENDIX  H:    LYELL  437 

experience  for  the  last  three  thousand  years  as  an  argument  against 
the  probability  of  such  occurrences  in  past  ages ;  but  it  is  not  pre- 
tended that  such  a  combination  can  be  foreseen. 

In  speculating  on  catastrophes  by  water,  we  may  certainly  antici- 
pate great  floods  in  future,  and  we  may  therefore  presume  that  they 
have  happened  again  and  again  in  past  times.  The  existence  of 
enormous  seas  of  fresh  water  such  as  the  North  American  lakes,  the 
largest  of  which  is  elevated  more  than  six  hundred  feet  above  the 
level  of  the  ocean,  and  is  in  parts  twelve  hundred  feet  deep,  is  alone 
sufficient  to  assure  us,  that  the  time  will  come,  however  distant,  when 
a  deluge  will  lay  waste  a  considerable  part  of  the  American  continent. 
No  hypothetical  agency  is  required  to  cause  the  sudden  escape  of  the 
confined  waters.  Such  changes  of  level,  and  opening  of  fissures,  as 
have  accompanied  earthquakes  since  the  commencement  of  the 
present  century,  or  such  excavation  of  ravines  as  the  receding  cataract 
of  Niagara  is  now  effecting,  might  breach  the  barriers.  Notwith- 
standing, therefore,  that  we  have  not  witnessed  within  the  last  three 
thousand  years  the  devastation  by  deluge  of  a  large  continent,  yet, 
as  we  may  predict  the  future  occurrence  of  such  catastrophes,  we  are 
authorized  to  regard  them  as  part  of  the  present  order  of  Nature,  and 
they  may  be  introduced  into  geological  speculations  respecting  the 
past,  provided  we  do  not  imagine  them  to  have  been  more  frequent 
or  general  than  we  expect  them  to  be  in  time  to  come. 

The  great  contrast  in  the  aspect  of  the  older  and  newer  rocks,  in 
their  texture,  structure,  and  in  the  derangement  of  the  strata,  ap- 
peared formerly  one  of  the  strongest  grounds  for  presuming  that  the 
causes  to  which  they  owed  their  origin  were  perfectly  dissimilar  from 
those  now  in  operation.  But  this  incongruity  may  now  be  regarded 
as  the  natural  result  of  subsequent  modifications,  since  the  difference 
of  the  relative  age  is  demonstrated  to  have  been  so  immense,  that, 
however  slow  and  insensible  the  change,  it  must  have  become  im- 
portant in  the  course  of  so  many  ages.  In  addition  to  the  volcanic 
heat,  to  which  the  Vulcanists  formerly  attributed  too  much  influence, 
we  must  allow  for  the  effect  of  mechanical  pressure,  of  chemical 
affinity,  of  percolation  by  mineral  waters,  of  permeation  by  elastic 
fluids,  and  the  action,  perhaps,  of  many  other  forces  less  understood, 
such  as  electricity  and  magnetism.  In  regard  to  the  signs  of  up- 
raising and  sinking,  of  fracture  and  contortion  in  rocks,  it  is  evident 
that  newer  strata  cannot  be  shaken  by  earthquakes,  unless  the  sub- 


438  A  SHORT  HISTORY  OF  SCIENCE 

jacent  rocks  are  also  affected;  so  that  the  contrast  in  the  relative 
degree  of  disturbance  in  the  more  ancient  and  the  newer  strata,  is 
one  of  many  proofs  that  the  convulsions  have  happened  in  different 
eras,  and  the  fact  confirms  the  uniformity  of  the  action  of  subter- 
ranean forces,  instead  of  their  greater  violence  in  the  primeval  ages. 

The  science  of  Geology  is  enormously  indebted  to  Lyett  —  more  so,  as  I  believe, 
than  to  any  other  man  who  ever  lived.  —  Darwin.     Autobiography. 

Pour  juger  de  ce  qui  est  arrive,  et  meme  de  ce  qui  arrivera,  nous  n'avons  qu'a 
examiner  ce  qui  arrive.  —  Buff  on.     Theorie  de  la  Terre. 


I.  SOME   INVENTIONS   OF  THE   EIGHTEENTH   AND   NINE- 
TEENTH CENTURIES.    APPLIED  SCIENCE  AND  ENGINEERING 

He  who  seeks  for  immediate  practical  use  in  the  pursuit  of  science,  may  be 
reasonably  sure  that  he  will  seek  in  vain.  Complete  knowledge  and  complete 
understanding  of  the  action  of  the  forces  of  nature  and  of  the  mind,  is  the 
only  thing  that  science  can  aim  at.  The  individual  investigator  must  find 
his  reward  in  the  joy  of  new  discoveries  ...  in  the  consciousness  of  having 
contributed  to  the  growing  capital  of  knowledge.  .  .  .  Who  could  have 
imagined,  when  Galvani  observed  the  twitching  of  the  frog  muscles  as  he 
brought  various  metals  in  contact  with  them,  that  eighty  years  later  Europe 
would  be  overspun  with  wires  which  transmit  messages  from  Madrid  to 
St.  Petersburg  with  the  rapidity  of  lightning,  by  means  of  the  same  principle 
whose  first  manifestations  this  anatomist  then  observed.  —  Helmholtz. 

The  place  of  inventions  in  the  history  of  science  is  hard  to  define. 
Conditioned  as  they  doubtless  are  by  a  favorable  environment  — 
at  least  for  survival  —  they  do  not  always  obviously  arise  as  a  direct 
or  logical  consequence  of  preceding  discoveries,  or  even  of  known 
principles,  but  seem  sometimes  to  spring  almost  de  novo  from  the  brain 
of  the  inventor.  And  yet  such  an  origin  is  probably  more  apparent 
than  real.  The  steam-engine  could  hardly  have  come  from  Watt 
without  Newcomen  and  Black  as  his  predecessors,  the  telegraph  from 
Morse  or  the  telephone  from  Bell  except  after  Franklin,  Oersted  and 
Faraday.  Probably  the  truth  is  that  if  we  only  knew  all  the  facts, 
instead  of  only  some  of  them,  we  should  find  every  invention  the 
natural  descendant,  near  or  remote,  of  science  already  existing.  And 
as  inheritance  often  seems  to  skip  a  generation  or  two  and  children 


APPENDIX  I:    INVENTIONS  439 

sometimes  show  no  discoverable  resemblance  to  their  immediate 
forbears,  so  inventions  may  come  without  disclosing  any  resemblance 
to  parent  inventions  or  ideas,  while  yet  really  intimately  related  to 
knowledge  that  has  gone  before. 

Nor  is  it  easy  to  estimate  the  reciprocal  debt  of  science  to  inventions 
and  the  arts.  That  this  debt  is  large  there  can  be  no  doubt.  To 
illustrate  this  fact  it  is  hardly  necessary  to  do  more  than  mention 
examples,  such  as  the  service  of  the  compass  to  the  sciences  of  geog- 
raphy, navigation  and  surveying ;  -of  the  telescope  and  the  chronom- 
eter to  astronomy ;  of  the  microscope  to  biology ;  of  the  air  pump 
to  natural  philosophy ;  or  of  the  abacus  or  the  Arabic  numerals  to 
arithmetic. 

Among  the  more  notable  of  the  inventions  of  the  nineteenth  cen- 
tury were  the  locomotive,  the  steamboat,  the  friction  match,  the 
sewing-machine,  the  steel  pen,  the  telegraph,  the  telephone  and  the 
phonograph ;  labor-saving  machinery ;  explosives ;  and  the  internal 
combustion  engine,  with  its  numerous  offspring  (motor  vehicles,  air- 
planes, motor  boats,  etc.). 

POWER  :  ITS  SOURCES  AND  SIGNIFICANCE.  —  The  recent  progress 
of  science  and  of  civilization  has  been  accompanied  by  a  remarkable 
extension  of  man's  control  over  his  environment,  which  has  come 
largely  with  his  ability  to  develop,  transmit,  and  utilize  chemical, 
gravitational  and  electrical  energy  or  power^.  The  ancients  and  the 
men  of  the  Middle  Ages  used  chiefly  the  power  of  man  and  other  ani- 
mals and  of  winds  (windmills)  and  to  some  extent  water  (i.e.  gravi- 
tation), as  in  water-wheels,  but  knew  little  of  heat  power  or  chemical 
power  and  nothing  of  electrical  power,  or  of  power  transmission  of 
any  kind, — except  in  moving  herds,  treadmills,  or  marching  armies. 

In  past  times  the  chief  store  of  national  power  was  manual  labor :  to-day 
it  is  the  machine  that  does  the  work.  —  K.  Pearson. 

The  first  step  in  the  modern  direction  was  apparently  toward  chemi- 
cal power,  in  the  invention  of  gunpowder. 

GUNPOWDER,  NITROGLYCERINE,  DYNAMITE.  —  Gunpowder  is  be- 
lieved to  have  been  known  to  the  Chinese  long  belong  it  appeared 
in  Europe.  An  explosive  mixture  of  charcoal,  sulphur,  and  nitre 
was  apparently  also  known  to  the  Arabians,  but  the  first  important 
appearance  of  gunpowder  in  Europe  was  about  the  fourteenth  cen- 
tury, and  since  the  sixteenth  it  has  played  an  all-important  part  in 


440  A  SHORT  HISTORY  OF  SCIENCE 

war  and  in  peace.  Its  effects  upon  society  and  civilization  have  been 
profound,  and  with  society  and  civilization  the  progress  of  science 
is  always  closely  bound  up. 

The  manufacture  of  gunpowder  marks  the  beginning  of  the  manu- 
facture of  power,  if  we  may  describe  the  controlled  accumulation, 
storage  and  liberation  of  energy  by  that  convenient  term.  In  1845 
gun-cotton  was  invented  by  Schonbein,  and  in  1847  nitroglycerine  by 
Sobrero,  and  both  explosives  were  found  to  be  far  more  copious  and 
powerful  sources  of  energy  than  gunpowder.  It  was  Alfred  Nobel, 
however,  a  Swedish  engineer,  who  after  mixing  nitroglycerine  with 
gunpowder  first  made  practical  use  of  this  for  blasting.  It  was  also 
Nobel  who  in  1867  made  nitroglycerine  less  dangerous  by  diluting  it 
with  inert  substances  such  as  silicious  earth,  —  mixtures  to  which  he 
gave  the  name  dynamite.1 

The  manufacture  of  power  from  gravitational  sources,  such  as 
water-power  and  wind  power,  goes  back  to  the  earliest  times  — 
sails,  wind-mills  and  water-wheels  being  of  very  ancient  origin. 
Power  from  fuel  begins  with  Newcomen,  Watt  and  the  steam- 
engine.  Electrical  power  is  at  present  chiefly  derived  indirectly 
from  gravitational  (hydraulic)  or  from  chemical  (fuel)  sources. 

THE  STEAM-ENGINE. — The  last  half  of  the  eighteenth  century  was 
not  merely  an  era  of  great  revolutions :  it  was  also  an  age  of  great 
inventions  and  among  these,  first  in  importance  as  well  as  first  to 
arise,  was  the  steam-engine. 

Various  and  more  or  less  successful  attempts  to  utilize  heat  or 
steam  as  a  source  of  power  had  been  made  before  Watt's  time,  such, 
for  example,  as  those  of  Hero  in  Alexandria  (120  B.C.)  the  Marquis 
of-  Worcester  (1663)  and  Newcomen  (1705).  Of  these  only  New- 
comen's  need  be  dwelt  upon  here.  In  Newcomen's  engine  a  vertical 
cylinder  with  piston  was  used,  the  piston-rod,  also  vertical,  being  fixed 
above  to  one  end  of  a  walking-beam  of  which  the  other  end  carried  a 
parallel  rod.  Thus  the  rise  and  fall  of  the  piston  caused  a  corre- 
sponding fall  and  rise  of  a  parallel  rod,  which  could  be  attached  to 
anything,  e.g.  to  a  pump.  The  cylinder  was  connected  with  a  steam 

1  Nobel  died  in  1896,  bequeathing  his  fortune,  estimated  at  $9,000,000,  to  the 
founding  of  a  fund  which  supports  the  international  "prizes"  —  usually  $40,000 
each  —  which  bear  his  name  and  are  annually  awarded  to  those  who  have  most 
contributed  to  "the  good  of  humanity."  Five  prizes  have  been  usually  given: 
viz.  one  in  physics,  one  in  chemistry,  one  in  medicine  or  physiology,  one  in 
literature  and  one  for  the  promotion  of  peace. 


APPENDIX  I :   INVENTIONS  441 

boiler  by  a  pipe  fitted  with  a  stopcock,  and  was  filled  with  steam  below 
the  piston  by  opening  the  stopcock.  The  steam  pressing  upon  the 
boiler  raised  the  piston  and  depressed  the  parallel  (pump)  rod.  The 
stopcock  was  then  closed,  a  "vent"  in  the  cylinder  was  opened,  cold 
water  was  introduced  from  another  pipe  to  condense  the  steam,  where- 
upon a  vacuum  formed,  and  the  atmospheric  pressure  depressed  the 
piston  and  lifted  the  pump  rod.  By  having  the  various  stopcocks 
carefully  worked  by  hand  a  certain  regularity  of  operation  could 
be  obtained,  but  before  long  improvements  were  made  and  the  stop- 
cocks were  caused  to  work  automatically.  But  since  the  cold  (con- 
densing) water  chilled  the  cylinder,  much  heat  was  necessarily  wasted. 

Watt  began  by  inventing  (in  1765)  a  separate  condenser,  for  cooling 
the  steam  without  cooling  the  cylinder,  —  thus  saving  a  vast  amount 
of  heat.  He  next  abandoned  altogether  the  use  of  atmospheric  pres- 
sure for  depressing  the  piston,  employing  steam  above  as  well  as 
below  the  piston,  to  lower  as  well  as  to  lift  it :  and  with  these  improve- 
ments, to  which  he  added  many  others,  he  soon  had  in  his  possession 
a  serviceable  and  automatic  steam-engine,  rudimentary  in  many 
respects,  but  not  essentially  unlike  that  of  to-day. 

THE  SPINNING  JENNY,  THE  WATER-FRAME  AND  THE  MULE. — In 
1770  James  Hargreaves  patented  the  spinning  jenny,  a  frame  with  a 
number  of  spindles  side  by  side,  by  which  many  threads  could  be 
spun  at  once  instead  of  only  one,  as  in  the  old,  one-thread,  distaff  or 
the  spinning  wheel.  In  1771  Arkwright  operated  successfully  in  a 
mill  a  patent  spinning  machine  which,  because  actuated  by  water 
power,  was  known  as  the  "water-frame."  In  1779  Crompton  com- 
bined the  principles  involved  in  Hargreaves'  and  Arkwright's  machines 
into  one,  which,  because  of  this  hybrid  origin,  became  known  as  the 
spinning  "mule."  This  proved  so  successful  that  by  1811  more  than 
four  and  a  half  million  spindles  worked  as  "  mules  "  were  in  operation 
in  England. 

A  similar  machine  for  weaving  was  soon  urgently  needed,  and  in 
1785  the  "power  loom"  of  Cartwright  appeared,  although  it  required 
much  improvement  and  was  not  widely  used  before  1813. 

THE  COTTON  GIN  (ENGINE).  —  With  the  inventions  just  described 
facilities  arose  for  the  manufacture  of  cotton  as  well  as  woollen,  but 
the  supply  of  raw  cotton  was  limited,  chiefly  because  of  the  difficulty 
of  separating  the  staple  (fibres)  from  the  seeds  upon  which  they  are 
borne.  Cotton  had  for  centuries  been  grown  and  manufactured  in 


442  A  SHORT  HISTORY  OF  SCIENCE 

India,  the  fibres  being  separated  from  the  seeds  by  a  rude  hand  ma- 
chine known  as  a  churka,  used  by  the  Chinese  and  Hindus.  By 
this  it  was  impossible  to  clean  cotton  rapidly.  The  invention  there- 
fore in  1793  by  Eli  Whitney  of  Connecticut  of  the  saw  cotton- 
gin  which  enormously  facilitated  this  separation  was  one  of  the 
most  important  inventions  ever  made.  This  consisted  in  a  series 
of  saws  revolving  between  the  interstices  of  an  iron  bed  upon  which 
the  cotton  was  so  placed  as  to  be  drawn  through  while  the  seeds  were 
left  behind.  The  value  of  the  saw  gin  was  instantly  recognized  and 
the  output  of  cotton  in  America  was  rapidly  and  immensely  increased 
by  its  use. 

STEAM  TRANSPORTATION.  —  Boats  and  ships  propelled  by  man 
power  or  by  the  wind  have  been  used  from  time  immemorial,  and 
parallel  rails  for  wheeled  conveyors  moved  by  animal  power  or  by 
gravity  preceded  the  steam  locomotive.  The  steamboat  and  the 
steam  vehicle  appeared  at  (or  in  the  case  of  the  latter  even  before) 
the  opening  of  the  nineteenth  century. 

The  first  practically  successful  steamboat  was  a  tug,  the  Charlotte 
Dundas,  built  and  operated  in  Soctland  for  the  towing  of  canal  boats 
by  Symmington  in  1802.  The  first  commercially  successful  steam- 
boat was  Fulton's  Clermont,  on  the  Hudson,  in  1807.  The  first 
steam-engine  to  run  on  roads  appears  to  have  been  Cugnot's  in  France 
in  1769.  The  first  to  run  on  rails  was  Trevithick's,  in  1804,  built  to 
fit  the  rails  of  a  horse  railway.  This  engine  also  discharged  its  exhaust 
steam  into  the  funnel  to  aid  the  draught  of  the  furnace,  —  a  device 
of  fundamental  importance  to  the  further  development  of  the  loco- 
motive. The  first  practically  successful  locomotive  was  Stephenson's 
Rocket  (1829). 

The  compound  (double  or  triple  expansion)  engine,  which  dates 
from  1781  (Hornblower),  1804  (Woolf),  and  1845  (McNaughton), 
embodies  what  is  perhaps  the  greatest  single  improvement  in  the 
steam-engine  in  the  nineteenth  century.  The  turbine  has  begun  to 
replace  the  reciprocating  engine  only  very  recently  (1900). 

THE  ACHROMATIC  COMPOUND  MICROSCOPE.  —  The  compound 
microscope,  after  its  introduction  about  the  middle  of  the  seventeenth 
century,  and  its  use  by  Malphigi,  Kircher,  Leeuwenhoek,  Grew,  and 
others,  was  of  only  limited  value  because  of  the  spherical,  and  espe- 
cially the  chromatic,  aberration  of  its  lenses.  This  remained  true 
until  long  after  Huygens  had  perfected  the  eye-piece  of  the  telescope, 


APPENDIX  I:    INVENTIONS  443 

and  Hall  and  Dolland  had  succeeded  in  correcting  chromatic  aberra- 
tion in  telescope  objectives  by  the  combination  of  crown  and  flint 
glass,  in  the  eighteenth  century. 

Amici,  of  Modena,  in  1812,  Fraunhofer  of  Munich  in  1816,  Tully 
of  London  in  1824,  J.  J.  Lister  in  1830  and  others  gradually  per- 
fected the  achromatic  microscope  objective,  so  that  about  1835  really 
excellent  instruments  became  accessible  to  microscopical  investiga- 
tors. The  numerous  discoveries  in  cellular  biology  and  in  pathology 
which  soon  followed  testify  to  the  extent  and  importance  of  these 
improvements. 

ILLUMINATING  GAS,  —  made  by  the  destructive  distillation  of  coal, 
was  invented  and  introduced  in  1792  by  William  Murdock,  who  in 
1802  had  so  far  perfected  the  process  that  even  the  exterior  of  his 
factory  in  Birmingham  was  illuminated  with  gas  in  celebration  of  the 
peace  of  Amiens. 

FRICTION  MATCHES, — were  preceded  early  in  the  nineteenth  century 
by  splinters  of  wood  coated  with  sulphur  and  tipped  with  a  mixture 
of  chlorate  of  potash  and  sugar.  These  when  touched  with  sulphuric 
acid  ignited.  It  was  not,  however,  until  1827  that  practical  friction 
matches  were  made  and  sold.  These  were  known,  after  their  inventor, 
as  "Congreves"  and  consisted  of  wooden  splints  coated  with  sulphur 
and  tipped  with  a  mixture  of  sulphide  of  antimony,  chlorate  of  potash, 
and  gum.  When  subjected  to  severe  friction,  specially  arranged  for, 
these  took  fire.  The  phosphorus  friction  match  was  introduced 
commercially  in  1833. 

THE  SEWING-MACHINE.  —  Very  few  labor-saving  inventions  sur- 
pass in  efficiency  sewing-machines.  These  also  were  invented  in 
the  nineteenth  century  and  had  a  gradual  development,  in  which 
various  inventors  participated.  The  first  which  need  be  mentioned 
was  that  of  a  French  tailor,  named  Thimonier,  patented  in  1830. 
It  is  said  that  although  made  of  wood  and  clumsy,  eighty  of  these 
machines  were  in  use  in  Paris  in  1841,  when  an  ignorant  mob  wrecked 
the  establishment  in  which  they  were  located  and  nearly  murdered 
the  inventor.  The  most  important  ideas  embodied  in  modern  ma- 
chines are,  however,  of  strictly  American  origin,  the  work  of  Walter 
Hunt  of  New  York,  and  of  Elias  Howe  of  Spencer,  Massachusetts 
being  of  principal  importance  (1846).  Other  Americans,  especially 
Singer,  Grover,  Wilson  and  Gibbs,  afterwards  contributed  to  the 
present  excellence  and  variety  of  the  sewing-machine. 


444  A  SHORT  HISTORY  OF  SCIENCE 

PHOTOGRAPHY.  —  Scheele,  the  Swedish  chemist,  appears  to  have 
been  the  first  to  study  the  effect  of  sunlight  on  silver  chloride.  Others, 
including  Rumford  and  Davy,  observed  the  chemical  properties  of 
light,  but  it  was  Wedgwood  who,  in  1802,  made  the  first  photograph 
by  throwing  shadows  upon  white  paper  moistened  with  nitrate  of 
silver.  Wedgwood  was  unable,  however,  to  fix  his  prints. 

Daguerreotypes,  taken  on  silver  plated  copper,  date  from  1839, 
and  were  made  by  covering  the  copper  with  a  thin  film  of  silver  iodide, 
—  a  compound  sensitive  to  light.  The  image  was  developed  by  mer- 
cury vapor  and  fixed  by  sodium  hyposulphite.  The  discovery  of  the 
fixing  power  of  hyposulphite  was  in  itself  alone  of  immense  impor- 
tance. With  the  name  of  Daguerre,  who  began  experimenting  in  1826, 
that  of  a  fellow  countryman  and  partner,  Niepce,  is  intimately  asso- 
ciated. 

The  subsequent  development  of  photography  is  due  to  a  host  of 
workers.  The  collodion  film  which  underlies  all  modern  work  was 
first  introduced  in  1850.  It  is  said  to  be  a  practically  perfect  medium 
because  totally  unaffected  by  silver  nitrate. 

ANAESTHESIA.  THE  OPHTHALMOSCOPE.  —  Anaesthesia,  or  insen- 
sibility to  pain,  during  dental  surgical  operations  was  introduced,  if 
not  discovered,  by  Wells,  a  dentist  of  Hartford,  Connecticut,  who 
himself  took  nitrous  oxide  gas  for  anaesthesia  in  1844.  The  first 
public  demonstration  of  surgical  anaesthesia  under  ether  was  made 
by  a  dentist,  Morton,  and  a  surgeon,  Jackson,  at  the  Massachusetts 
General  Hospital  in  Boston  in  1846.  Anaesthesia  by  chloroform  was 
introduced  by  Simpson  of  Edinburgh,  in  1847. 

The  ophthalmoscope,  an  instrument  for  examination  of  the  inte- 
rior of  the  eye,  of  inestimable  value  to  medicine,  was  invented  by 
Helmholtz  in  1851.  It  is  said  that  when  von  Graefe,  an  eminent 
ophthalmologist,  first  saw  with  it  the  interior  of  the  eye  he  cried  out, 
"Helmholtz  has  unfolded  to  us  a  new  world." 

INDIA-RUBBER,  —  the  coagulated  and  dried  juice  of  the  rubber 
tree,  first  reported  by  Herrera, "  who  in  the  second  voyage  of  Columbus 
observed  that  the  inhabitants  of  Hayti  played  a  game  with  balls  made 
'of  the  gum  of  a  tree'  and  that  the  balls  although  large  were  lighter, 
and  bounced  better,  than  the  windballs  of  Castile,"  was  at  the  end  of 
the  eighteenth  century  still  a  curiosity,  employed  by  Priestley,  among 
others,  as  an  eraser  or  "rubber." 

Rubber  is  a  hydrocarbon  soft  when  pure  but  readily  hardened  by 


APPENDIX  I:   INVENTIONS  445 

"  vulcanization,"  i.e.  treatment  with  sulphur  or  certain  sulphur  com- 
pounds (chloride,  carbon  bisulphide),  a  process  introduced  by  Good- 
year in  1839. 

ELECTRICAL  APPARATUS;  TELEGRAPH,  TELEPHONE,  ELECTRIC 
LIGHTING,  ELECTRIC  MACHINERY.  —  The  first  important  applica- 
tion of  electricity  to  the  service  of  man  was  the  telegraph.  This  is 
too  well  known  to  require  more  than  the  briefest  description.  An 
electric  circuit  in  a  wire  "made"  or  "broken"  at  one  point  is  likewise 
made  or  broken  at  all  other  points.  Hence,  it  is  only  necessary  to 
employ  a  preconcerted  system  of  make-and-break  signals  to  dispatch 
messages.  This  plan  was  first  employed  in  1836  by  S.  F.  B.  Morse, 
a  native  of  Charlestown,  Massachusetts,  and  the  first  telegraph  line 
between  two  cities  was  installed  between  Baltimore  and  Washington 
in  1844.  The  first  transatlantic  cable  was  laid  in  1858. 

The  telephone,  invented  by  Alexander  Graham  Bell,  is  even  more 
familiar.  This,  also,  depends  on  the  making  and  breaking  of  an  elec- 
tric circuit,  not  (as  is  usual  in  the  telegraph)  by  a  key  manipulated  by 
the  finger,  but  by  sound  waves  of  the  human  voice  impinging  upon  a 
delicate  membrane  (the  transmitter)  and  reproduced  at  a  distance  by 
corresponding  vibrations  of  another  delicate  membrane  (the  receiver). 

Wireless  telegraphy  and  wireless  telephony  differ  from  ordinary 
telegraphy  and  telephony  merely  in  the  use  of  signal  waves  set  up  in 
the  ether  instead  of  signal  waves  (i.e.  making  and  breaking)  set  up  in 
the  current  carried  by  a  wire.  Both  arts  are  inventions  of  very  recent 
date. 

The  electric  light,  which  had  long  been  known  as  a  laboratory 
experiment,  became  of  practical  utility  about  1880,  with  the  inven- 
tion of  the  incandescent  lamp,  first  the  carbon  arc  and  then  the  car- 
bon filament,  the  former  by  Brush,  the  latter  by  Edison. 

The  phonograph  was  invented  by  Edison  in  1876,  and  was  the 
culmination  of  attempts  extending  over  many  years  to  record  and 
reproduce  sound  waves.  In  these  attempts  Young,  Konig,  Fleeming 
Jenkin  and  many  others  participated. 

FOOD  PRESERVING  BY  CANNING  AND  REFRIGERATION.  —  In  1810 
Appert  of  France  succeeded  in  preserving  foods  in  closed  vessels  by 
heating  and  sealing  while  hot.  In  1816  a  small  amount  of  food  pre- 
served in  this  way  found  its  way  into  the  British  Navy,  where  its 
value  was  recognized  to  some  extent  as  a  preventive  of  scurvy.  It  was 
not,  however,  until  after  the  American  Civil  War  that  the  industry 


446  A  SHORT  HISTORY  OF  SCIENCE 

began  to  assume  anything  like  the  vast  extent  and  importance  it  has 
since  reached. 

Refrigeration  in  various  forms  has  been  used  for  food  preserving 
probably  from  the  earliest  times,  but  the  present  enormous  industry 
of  cold  storage  has  all  grown  up  since  the  middle  of  the  nineteenth 
century  with  the  invention  and  development  of  refrigerators  (domestic 
and  commercial)  and  especially  of  machines  for  producing  and  dis- 
tributing compressed  air  or  other  vapors  or  brine  ammonia  and  other 
liquids  at  very  low  temperatures.  These  have  been  perfected  rather 
rapidly  since  1860,  but  did  not  become  common  before  1880.  The 
first  cargo  of  fresh  meat  successfully  exported  from  America  to  Europe 
was  shipped  in  March,  1879,  and  from  New  Zealand  to  Europe  in 
February,  1880,  arriving  after  a  passage  of  98  days  in  excellent 
condition. 

THE  INTERNAL-COMBUSTION  ENGINE.  —  For  a  century  or  there- 
abouts the  steam-engine  stood  without  a  rival  as  a  thermodynamic 
machine  and  prime  mover.  Innumerable  attempts  had  been  made 
meantime  to  construct  other  kinds  of  engines  to  convert  heat  more 
directly  into  power  for  mechanical  work;  but  it  was  not  until  1876 
that  the  internal-combustion  engine  as  improved  by  Otto  became  a 
practical  success. 

In  the  steam-engine,  the  furnace  in  which  the  heat  is  generated  is 
external  to  the  cylinder  in  which  that  heat  does  its  work,  the  steam 
being  merely  an  intermediary.  It  is  therefore  an  external-combus- 
tion engine.  Obviously,  if  the  fuel  burned  is  made  to  liberate  its 
heat  in  the  cylinder  instead  of  the  furnace,  the  steam  can  be  dis- 
pensed with.  This  is  what  actually  happens  in  the  internal-com- 
bustion engine.  The  present  enormous  extent  of  the  use  of  such 
engines  for  motors  of  all  kinds,  testifies  to  the  importance  of  this 
invention. 

ANILINE,  —  was  first  obtained  from  indigo  in  1826  by  Unverdorben 
and  named  by  him  crystalline.  In  1834  Runge  prepared  a  similar 
substance  from  coal  tar,  and  in  1841  Fritsche  obtained  from  indigo 
an  oil  which  he  called  aniline,  —  a  word  derived  from  the  Sanskrit 
Nila,  the  indigo  plant.  The  commercial  importance  of  aniline  in  the 
dye-stuffs  industry  dates  from  the  discovery  of  mauve  by  Perkin  in 
1858.  This  was  the  first  of  the  notable  series  of  aniline  dyes  now  so 
well  known,  and  the  forerunner  of  the  immense  color  industry  of  to-day. 

THE  MANUFACTURE  OF  STEEL;  BESSEMER.  —  The  making  of  steel 


APPENDIX  I:    INVENTIONS  447 

by  the  decarbonization  of  cast-iron,  a  process  which  initiated  what 
has  been  called  the  "age  of  steel,"  was  introduced  by  Bessemer  (1813- 
1898)  in  1856.  Bessemer's  attention  was  drawn  to  the  subject  by 
his  recognition  of  the  necessity  of  improving  gun-metal.  Bessemer's 
process  was  at  first  only  partially  successful,  but  since  others  have 
shown  how  to  improve  it  (by  the  addition  of  spiegeleisen,  etc.)  it 
has  reached  enormous  proportions. 

AGRICULTURAL  APPARATUS  AND  INVENTIONS.  —  Beginning  about 
1850  an  era  of  improved  agricultural  apparatus  began,  of  which  one 
result  has  been  the  opening  of  vast  tracts  of  farm  lands  which  might 
otherwise  have  remained  unproductive.  Steel  plows,  better  harrows, 
mowing-machines,  horse-power  rakes,  haymaking  machinery,  and 
especially  harvesters  of  ingenious  design  for  cereal  crops  (first  intro- 
duced by  McCormick  in  1834),  threshing-machines  and  spraying- 
machines  are  to-day  common,  where  these  were  almost  unknown 
before  1875.  Machinery  has  also  been  applied  to  dairying,  first  to  the 
making  of  butter  and  cheese,  and  more  recently  even  to  the  milking 
of  cows.  Progress  has  also  been  made  in  the  preservation  of  milk  and 
of  eggs  by  condensing,  drying,  freezing,  etc.  by  new  and  economical 
processes  invented  and  applied  since  that  time. 

APPLIED  SCIENCE.  ENGINEERING.  —  Very  much  as  discoveries 
and  inventions  blend  together  and  as  both  spring  from  a  common 
source,  manifested  as  curiosity,  inquiry,  experimentation  and  cor- 
relation (i.e.  from  science),  so  applied  science,  including  engineering, 
comes  from  a  common  ancestry,  i.e.  from  correlated  knowledge, — 
which  is  science.  Both  terms  are  loosely  used  and  both  cover  to-day 
a  multitude  of  diversified  human  activities. 

With  the  progress  of  science,  arts  and  invention,  engineering  and 
other  forms  of  applied  science  have  developed  so  that  these  frequently 
have  their  own  schools,  either  with  or  apart  from  universities  and 
colleges ;  the  school  for  miners  at  Freiberg,  in  Saxony,  begun  in  1765, 
being  now  only  one  of  hundreds  of  technological  and  scientific  schools 
for  the  training  of  engineers  and  others.  Up  to  1850  most  engineers 
in  America  were  trained  in  military  schools  and  were  primarily  military 
engineers.  But  from  that  time  forward  the  civil,  as  opposed  to  the 
military,  engineer  began  to  appear,  and  from  the  parent  stem  of  civil 
engineering  we  now  have  mechanical,  mining,  electrical,  sanitary, 
chemical,  marine  and  other  branches  of  engineering,  often  highly 
specialized.  The  term  "  engineer"  is  now  very  widely  employed,  with 


448  A  SHORT  HISTORY  OF  SCIENCE 

more  or  less  appropriateness,  to  occupations  remote  from  those  of  the 
military  or  civil  engineer,  as  for  example,  the  "illuminating  engineer, " 
the  "  efficiency  engineer,"  the  "  public  health  engineer,"  etc.  We  may 
soon  expect  to  have  added  to  these  many  others,  such  as  the  agricul- 
tural engineer,  the  forest  engineer  and  even  the  fishery  engineer. 

An  historical  sketch  of  applied  science  and  engineering  would  ob- 
viously include  the  work  of  Archimedes,  Vitruvius,  Frontinus,  and 
Leonardo,  and  proceed  with  the  applications  made  of  the  discov- 
eries and  inventions  of  the  Renaissance  and  modern  times.  Some  of 
this  ground  is  covered  in  the  present  volume,  and  more  of  it  in  the 
series  of  books  by  Smiles  entitled  Lives  of  the  Engineers. 

—  There  is  scarcely  a  department  of  science  or  art  which  is  the  same,  or  at  all  the 
same,  as  it  was  fifty  years  ago.     A  new  world  of  inventions  —  of  railways  and  of 
telegraphs  —  has  grown  up  around  us  which  we  cannot  help  seeing;  a  new  world 
of  ideas  is  in  the  air  and  affects  us,  though  we  do  not  see  it. 

—  Bagehot.     Physics  and  Politics  (1868). 

—  Only  since  continental  ideas  and  influences  have  gained  ground  in  this  country 
(Great  Britain')  has  the  word  science  gradually  taken  the  place  of  that  which  used 
to  be  termed  natural  philosophy  or  simply  philosophy.     One  reason  why  science 
forms  such  a  prominent  feature  in  the  culture  of  this  age  is  the  fact  that  only 
within  the  last  hundred  years  has  scientific  research  approached  the  more  intricate 
phenomena  and  the  more  hidden  forces  and  conditions  which  make  up  and  govern 
our  everyday  life.     The  great  inventions  of  the  sixteenth,  seventeenth  and  eighteenth 
centuries  were  made  without  special  scientific  knowledge,  and  frequently  by  persons 
who  possessed  skill  rather  than  learning.     They  greatly  influenced  science  and 
promoted  knowledge,  but  they  were  brought  about  more  by  accident  or  by  the  prac- 
tical requirements  of  the  age  than  by  the  power  of  an  unusual  insight  acquired  by 
study.     But  in  the  course  of  the  last  hundred  years  the  scientific  investigation  of 
chemical  and  electric  phenomena  has  taught  us  to  disentangle  the  intricate  web  of 
the  elementary  forces  of  nature,  to  lay  bare  the  many  interwoven  threads,  to  break  up 
the  equilibrium  of  actual  existence,  and  to  bring  within  our  power  and  under  our 
control  forces  of  undreamed-of  magnitude.     The  great  inventions  of  former  ages 
were  made  in  countries  where'  practical  life,  industry  and  commerce  were  most 
advanced;  but  the  great  inventions  of  the  last  fifty  years  in  chemistry  and  electricity 
and  the  science  of  heat  have  been  made  in  the  scientific  laboratory:  the  former 
were  stimulated  by  practical  wants;  the  latter  themselves  produced  new  practical 
requirements,  and  created  new  spheres  of  labor,  industry,  and  commerce.     Science 
and  knowledge  have  in  the  course  of  this  century  overtaken  the  march  of  practical 
life  in  many  directions.  —  Merz. 


SKETCH  MAP  SHOWING  PLACES 
IMPORTANT  IN  ANCIENT  AND  MFDIAEVAL  SCIENCE 


SOME  IMPORTANT  NAMES,  DATES  AND  EVENTS  IN  THE 
HISTORY  OF  SCIENCE  AND  CIVILIZATION 

(For  certain  earlier  events,  see  Chapters  I  and  II.) 
c.  =  circa,  about. 


SCIENCE 

GENERAL 

HISTORY,   LITERATURE, 
ART,  ETC. 

c.  2000-1700.  Ahmes  Papyrus. 

c.  1100. 

Gades   (  Cadiz}   founded 

by  the  Phoenicians. 

c.  1000. 

Homer.  David.  Solomon. 

c.  850. 

Carthage  founded. 

. 

c.  800. 

Hesiod. 

P 

c.  753. 

Home  founded   (legend- 

ary}. 

c.  700. 

Nineveh  flourishes  under 

2    c.  640-546. 

«    c.  611-545. 
bo 

Thales. 
Anaximander. 

c.  660. 
610. 

Sennacherib. 
Byzantium  founded. 
Sappho  and  other  Greek 

J§ 

poets. 

« 

Necho  II  undertakes  to 

«S 

connect  River  Nile  and 

« 

Red  Sea  by  Canal.  His 

sailors  circumnavigate 

Africa. 

0 

c.  606. 

Nineveh  destroyed. 

*    c.  588-524. 

Anaximenes. 

c.  600. 

Marseilles  founded. 

S    c.  582-500. 

Pythagoras. 

c.  660. 

Crcesus  and  Solon. 

g    c.  576-480. 

Xenophanes. 

c.  550-478. 

Confucius. 

2    c.  540-475. 

Heraclitus. 

c.  538. 

Babylon  taken  by  Cyrus. 

tj    c.  539. 

p 

Parmenides. 

525-456. 

JEschylus. 

c.  500. 

Alcinseon. 

c.  500. 

Carthaginians      explore 

c.  600-428. 

Anaxagoras. 

west  coast  of  Africa. 

c.  470. 

Hippocrates  of  Chios 

490-429. 

Pericles. 

(  Mathematician)  . 

490. 

Marathon,  Battle  of. 

«        469-399. 

Socrates. 

c.  484-425. 

Herodotus. 

£  c.  465. 

Empedocles. 

480. 

Thermopylae,  Battle  of. 

§  c.  460. 

Leucippus. 

480. 

Salamis,  Battle  of. 

1    c.  460-370. 

Democritus. 

2    c.  460. 

Hippocrates    of    Cos 

480-406. 

Euripides.     Phidias. 

its 

(Physician). 

450-385. 

Aristophanes. 

fe   c.  428-347. 

Archytas. 

427-347. 

Plato. 

450-400. 

Thucydides. 

c.  420. 

Hippias. 

c.  434-359. 

Xenophon. 

c.  408-? 

Eudoxus. 

c.  430. 

The  plague  at  Athens. 

2G 

449 

450 


A  SHORT  HISTORY  OF  SCIENCE 


SCIENCE 

GENERAL 

HISTORY,  LITERATURE, 
ART,  ETC. 

c.  400. 

Meton  (Calendar). 

c.  400. 

Motion      of      Earth 

(Philolaus). 

384-322. 

Demosthenes. 

c.  370. 

Diogenes.  Scopas.   Prax- 

o 
pq 

384-322. 

Aristotle. 

iteles. 

375-325. 

Mensechmus. 

356-323. 

Alexander  the  Great. 

c.  375. 

Heraclides  of  Pontus. 

338. 

Chceronea,  Battle  of. 

i 

372-287. 

Theophrastus. 

c.  350-260. 

Zeno  (Stoic). 

332. 

Alexandria  founded. 

g 

342-270. 

Epicurus. 

& 

c.  330-275. 

Euclid. 

c.  325. 

Eudemus. 

323-30. 

The  Ptolemies,  I-  VI. 

c.  300. 

Museum  and  Library  of 

Alexandria. 

300. 

Epicurus. 

§ 

283. 

The    Pharos     built    at 

c.  300. 

Herophilus.  Erasistra- 

Alexandria. 

d 

tus. 

280. 

The  Colossus  of  Rhodes. 

M 

287-212. 

Archimedes. 

| 

c.  276-194. 

Erastosthenes. 

270- 

Aristarchus. 

c.  285. 

Theocritus. 

S 

c.  260-200. 

Apollonius. 

2 

238. 

Decree    of    Canopus 

269. 

Silver  money  first  coined 

(Leap  Tear). 

in  Rome. 

c.  210. 

The  Great  Chinese  Wall 

begun. 

Paper  made  in  China. 

. 

c.  170. 

Polybius. 

pq 

c.  166. 

Terence. 

& 

161. 

Philosophers  and  Rheto- 

3 

c.  135. 

Ctesibius. 

ricians  banished  from 

0 

c.  146-126. 

Hipparchus. 

Rome. 

"a 

146. 

Carthage    destroyed   (re- 

1 

built  in  123). 

CHRONOLOGY 


451 


SCIENCE 


GENERAL  HISTORY,  LITERATURE, 
ART,  ETC. 


98-55.         Lucretius, 
c.  70-  Geminus. 

c.  63  B.C.-24A.D. 

Strabo. 
Varro. 

47.  Julian  Calendar. 

14.  Vitruvius.    De  Archi- 

tectura. 


c.  75. 


%  c.  130. 
<3  c.  140. 
§  c.  140. 


|>  c.  250. 
£   c.  300. 


c.  370. 


106-43.       Cicero. 
102-44.       Caesar. 

59  B.C.-17  A.D. 

Livy. 
54  B.C.-39  A.D. 

Seneca. 

47.  Ccesar  takes  Alexandria. 

39.  Pollio  founds  First 

Public  Library. 

27.  End  of  Roman  Republic. 

Golden  Age  of  Roman 
Literature.  (Horace, 
Virgil,  Livy,  etc.) 


Nicomachus. 

23-79.         Pliny, 
c.  40-103.       Frontinus. 


Hero. 


Galen. 

Ptolemy.  (Almagest.) 

Theon  of  Smyrna. 


Diophantus. 
Pappus. 


272-337.       Constantino        (First 
Christian  Emperor). 


Theon  of  Alexandria. 


354-430.       St.  Augustine. 


452 


A  SHORT  HISTORY  OF  SCIENCE 


SCIENCE 


GENERAL  HISTORY,  LITERATURE, 
ART,  ETC. 


I 


410-485.     Proclus. 

476.  Brahmagupta. 

Martianus    Capella 
(Liberal  Arts). 


c.  480-524.     Boethius. 
c.  630.  Arya-bhata. 


•§,       781-790.      Schools  of  Alcuin. 


c.  830.          Algebra  of  Alkarismi. 


940-1003.     Gerbert    (Pope    Syl- 

vester  II). 
980-1037.    Avicenna. 


c.  1000. 
c.  1038. 


Bhaskara. 
Alhazen. 


476. 


Fall  of  Rome. 


529.  Edict    of    Justinian. 

Schools     of     Athens 

closed. 
569-632.      Mohammed. 


641. 


711. 


732. 


c.  742-814. 


The  Hegira. 

Fall  of  Alexandria. 


Moorish  Conquest    of 

Spain. 
Moorish  Invasion  of 

Western        Europe 

checked   by  Charles 

Martel. 
Charlemagne. 


962. 


Holy  Boman  Empire. 
Abelard. 


1066.  Battle  of  Hastings. 

1096-1270.    Crusades. 


CHRONOLOGY 


453 


SCIENCE 

GENERAL  HISTORY,  LITERATURE, 
ART,  ETC. 

Arabic  numerals. 

x 

1113-1150. 

Translations        of 

a 

Greek       Classics 

I 

from  Arabic. 

ji 

1126-1198. 

Averroes. 

a 

Jordanus     Nemora- 

O 

i 

rius. 

H 

1175. 

Pisano  (Fibonacci)- 

1206-1280. 

Albertus  Magnus. 

1210. 

Aristotle's    Physics 

1215. 

Magna  Charta. 

proscribed          in 

c.  1254-1324. 

Marco  Polo. 

Paris. 

1265-1321. 

Dante  Alighieri. 

- 

1214-1294. 

Roger  Bacon. 

<1> 

c.  1219. 

University   of    Bo- 

I 

logna. 

c.  1300. 

Spectacles  invented. 

1249. 

University   College, 

H 

Oxford. 

1284. 

Peterhouse  College, 

Cambridge. 

Mongolian  Observa- 

tory at  Meraga. 

1304-1374. 

Petrarch. 

^ 

1337-1453. 

The   Hundred    Tears' 

I 

1364. 

University      of 

War. 

1 

Vienna. 

c.  1340-1400. 

Chaucer. 

& 

1340-1450. 

The  Black  Death. 

9 

1379-1446. 

Brunelleschi. 

1401-1464. 

Nicolas  of  Cusa. 

1423-1461. 

Peurbach. 

b 

1436-1476. 

Regiomontanus. 

1444-1511. 

Bramante. 

I 

Tartar   Observatory 

c.  1450. 

Invention  of  Printing. 

(Samarcand). 

1453. 

Fall  of  Constantinople 

^ 

1452-1519. 

Leonardo  da  Vinci. 

to  the  Turks. 

a 
• 

1473-1543. 

Copernicus. 

1471-1528. 

Diirer. 

1 

1486-1567. 

Stifel. 

1492. 

Discovery  of  America. 

& 

1490-1555. 

Agricola. 

1497. 

Vasco  da  Gama  rounds 

1493-1541. 

Paracelsus. 

Cape  of  Good  Hope. 

1 

1501-1676. 

Cardan. 

1 

1503. 

Margarita  philoso- 

w 

phica. 

454 


A  SHORT  HISTORY  OF  SCIENCE 


SCIENCE 

GENERAL  HISTORY,  LITERATURE, 
ART,  ETC. 

1510-1558. 

Recorde. 

1513. 

Balboa  reaches  Pacific 

c.  1506-1559. 

Tartaglia. 

Ocean. 

1510-1589. 

Palissy. 

1517. 

Protestant      Reforma- 

1512-1594. 

Mercator. 

tion. 

1514-1564. 

Vesalius. 

1519-1522. 

First       Circumnaviga- 

1514-1576. 

Rheticus. 

tion  of  the  Globe  by 

1616-1565. 

Gesner. 

Magellan. 

1522-1565. 

Ferrari. 

1524-1680. 

Camoens. 

1540-1603. 

Vieta. 

1530. 

Spinning  wheel. 

cfc 

1543. 

De    JRevolutionibus 

1547-1616. 

Cervantes.* 

1 

of  Copernicus. 

c.  1552-1599. 

Spenser. 

1543-1616. 

Baptista  della  Porta. 

1564-1616. 

Shakespeare. 

J 

1544-1603. 

Gilbert. 

1673-1637. 

Ben  Jonson. 

w 

1546-1601. 

Tycho  Brahe. 

b 

1548-1600. 

Bruno. 

§ 

1548-1620. 

Stevinus. 

1688. 

Defeat  of  the  Spanish 

0 

1550-1617. 

Napier. 

Armada. 

•£ 

1560-1621. 

Harriott. 

1598. 

Edict  of  Nantes. 

-3 

1561-1626. 

Francis  Bacon. 

CO 

1564-1642. 

Galileo. 

1600-1681. 

Calderon. 

1571-1630. 

Kepler. 

1575-1660. 

Oughtred. 

1577-1644. 

Van  Helmont. 

1578-1667. 

W.  Harvey. 

1582. 

Gregorian      Calen- 

dar. 

1591-1626. 

Snellius. 

1593-1662. 

Desargues. 

1696-1650. 

Descartes. 

1598-1647. 

Cavalieri. 

1601-1666. 

Fermat. 

1602-1686. 

Von  Guericke. 

1605. 

Don  Quixote. 

1608-1647. 

Torricelli. 

1607. 

First  Permanent  Eng- 

1616-1703. 

Wallis. 

lish     Colony    in 

1623-1662. 

Pascal. 

America. 

0 

1624-1689. 

Sydenham. 

1608-1774. 

Milton. 

1627-1691. 

Boyle. 

1618-1648. 

Thirty  Years'  War. 

I 

1629-1695. 

Huygens. 

1622-1673. 

Moliere. 

« 

1630-1677. 

Barrow. 

1631-1700. 

Dryden. 

1 

1635-1703. 

Hooke. 

1636. 

Harvard      College 

CO 

1635-1672. 

Willughby. 

founded. 

1642-1727. 

Newton. 

1638-1715. 

Louis  XIV. 

1646-1716. 

Leibnitz. 

1639-1699. 

Racine. 

CHRONOLOGY 


455 


SCIENCE 

GENERAL  HISTORY,  LITERATURE, 
ART,  ETC. 

1637. 

Discours  sur  la  Me- 

1649-1660. 

English     Common- 

§ 

thode.     (Analytic 

wealth. 

1 

Geometry.) 

s 

1644-1710. 

Roemer. 

§ 

1656-1742. 

Halley. 

1660-1731. 

DeFoe. 

fr 

1660-1734. 

Stahl. 

3 

£ 

1668-1738. 

Boerhaave. 

1672-1725. 

Peter  the  Great 

1 

1677-1761. 

Hales. 

| 

1687. 

Principia  of   New- 

1683. 

Siege  of  Vienna  by 

1 

ton.       -* 

Turks. 

-4-» 

1698-1746. 

Maclaurin. 

1688-1744. 

Pope. 

« 

1699-1739. 

Dufay. 

1694-1778. 

Voltaire. 

CO 

1699-1777. 

Jussieu. 

1700-1782. 

Beraouilli,  D. 

1705. 

Newcomen's   .En- 

gine. 

1706-1790. 

Franklin. 

1707-1778. 

Linnaeus. 

1707-1783. 

Euler. 

1707-1788. 

Buffon. 

1707-1777. 

Haller. 

1709-1784. 

Samuel  Johnson. 

1717-1783. 

d'Alembert. 

1711-1776. 

Hume. 

1726-1797. 

Hutton. 

1728-1793. 

Hunter. 

1728-1774. 

Goldsmith. 

1731-1810. 

Cavendish. 

1732-1790. 

Washington. 

£ 

1733-1804. 

Priestley. 

1 

1736-1813. 

Lagrange. 

s 

1736-1819. 

Watt. 

1737-1794. 

Gibbon. 

,ej 
-«-> 

1738-1822. 

Herschel,  F.  W. 

1 

1742-1786. 

Scheele. 

M 

1743-1794. 

Lavoisier. 

W 

1744-1829. 

Lamarck. 

1746-1818. 

Monge. 

'  1749-1827. 

Laplace. 

1749-1832. 

Goethe. 

1750-1817. 

Werner. 

1762-1833. 

Legendre. 

1759-1796. 

Burns. 

1753-1814. 

Rumford. 

1759-1805. 

Schiller. 

1764. 

Watt's  Steam   En- 

gine. 

1766-1844. 

Dalton. 

1767. 

Spinning  Jenny. 

1769-1832. 

Cuvier. 

1769-1859. 

Humboldt. 

1769-1821. 

Napoleon  I. 

456 


A  SHORT  HISTORY  OF  SCIENCE 


SCIENCE 

GENERAL  HISTORY,  LITERATURE, 
ART,  ETC. 

1769. 

Spinning  Frame. 

1770-1850. 

Wordsworth. 

1773-1829. 

Young. 

1771-1832. 

Scott. 

1774. 

Discovery    of   Oxy- 

1772-1834. 

Coleridge. 

gen. 

1773-1859. 

Metternich. 

1775-1836. 

Ampere. 

1775-1781. 

American  Revolution. 

1776-1839. 

Treviranus. 

1777-1855. 

Gauss. 

£ 

1778-1829. 

Davy. 

§ 

1778-1841. 

De  Candolle. 

•| 

1779-1848. 

Berzelius. 

I 

1781-1848. 

Stephenson. 

"•" 

1781. 

Discovery    of    Ura- 

M* 

nus. 

•g 

1783. 

Air  Balloon. 

p 

1784-1846. 

Bessel. 

1789-1794. 

French  Revolution. 

t5 

Parallax  of  stars. 

1 

1791-1867. 

Faraday. 

i 

1791-1872. 

Morse. 

i 

1792. 

Cotton  Gin. 

1792-1822. 

Shelley. 

1792-1876. 

von  Baer. 

1793-1856. 

Lobatchewski. 

1794. 

Ecole    Poly  tech- 

1795-1821. 

Keats. 

nique. 

1795-1881. 

Carlyle. 

1796. 

Vaccination. 

1796-1832. 

Carnot. 

1799-1853. 

St.  Hilaire. 

1801-1858. 

Miiller. 

1803-1873. 

Liebig. 

1802-1885. 

Victor  Hugo. 

1807-1873. 

Agassiz,  L. 

1802-1894. 

Kossuth. 

1809-1882. 

Darwin. 

1803-1882. 

Emerson. 

1810-1888. 

Gray,  Asa. 

1804-1865. 

Cobden. 

l 

1811-1877. 

Leverrier. 

1805. 

Battle  of  Trafalgar. 

a 

1811-1899. 

Bunsen. 

1805-1872. 

Mazzini. 

3 

1813-1878. 

Bernard. 

1807-1882. 

Longfellow. 

^ 

1813-1898. 

Bessemer. 

1807-1882. 

Garibaldi. 

« 

1817-1911. 

Hooker. 

1807-1892. 

Whittier. 

a 

1818-1889. 

Joule. 

1809-1865. 

Lincoln. 

g 

1819-1892. 

Adams. 

1809-1892. 

Tennyson. 

1820-1903. 

Spencer. 

1810-1861. 

Cavour. 

1820-1910. 

Florence      Nightin- 

1811-1863. 

Thackeray. 

gale. 

1812-1870. 

Dickens. 

1821-1894. 

Helmholtz. 

1815. 

Battle  of  Waterloo. 

1822-1882. 

Mendel. 

1815-1898. 

Bismarck. 

CHRONOLOGY 


457 


SCIENCE 

GENERAL  HISTORY,  LITERATURE, 
ART,  ETC. 

1822-1888. 

Clausius. 

1834. 

Poor  Law  Eeform  in 

1822-1895. 

Pasteur. 

England. 

1822-1908. 

Gibbs. 

1837. 

Accession     of     Queen 

1823-1913. 

Wallace. 

Victoria. 

1824-1887. 

Kirchhoff. 

1846-1848. 

War    between    United 

1824-1907. 

Kelvin. 

States  and  Mexico. 

1825-1894. 

Huxley. 

1846. 

Eepeal    of    the     Corn 

1827-1914. 

Lister. 

Laws. 

1828. 

Synthesis  of  Urea. 

1848. 

Abdication     of    Louis 

1828. 

Stephensorf  s 

Philippe  of  France. 

"Eocket." 

1852. 

Accession  of  Napoleon 

1829-1896. 

Kekule". 

III. 

1830. 

LyelVs  Principles 

1853-1856. 

Crimean  War. 

of  Geology. 

1854. 

First   (Perry)     Treaty 

1831-1879. 

Maxwell. 

between  United  States 

^^ 

1834-1906. 

Langley. 

and  Japan. 

•e 

1834-1907. 

Mendeleeff. 

1859- 

William  II  of  Germany. 

•1 

1834-1914. 

Weismann. 

1859. 

Peace  of  Villafranca. 

§ 

1835-1909. 

Newcomb. 

1861. 

First    Italian    Parlia- 

§ 

1836. 

The  Telegraph. 

ment. 

1 

1838-1907. 

Perkin. 

1861-1865. 

Civil  War  in  the  United 

•J2 

1839. 

The  Daguerreotype. 

States. 

0 

1843-1910. 

Koch. 

1866. 

War   between    Prussia 

3 

1846. 

Anaesthesia. 

and  Austria. 

I 

Discovery   of  Nep- 

1867. 

End  of  the  Shogunate 

1 

tune. 

of  Japan. 

to 

1847- 

Graham  Bell. 

1870-1871. 

War    between  Prussia 

1847. 

Die  Erhaltung  der 

and  France. 

Kraft. 

1890. 

Promulgation  of  Con- 

1847- 

Edison. 

stitution  of  Japan. 

1848- 

De  Vries. 

1894. 

War     between     China 

1852- 

Van't  Hoff. 

and  Japan. 

1857-1894. 

Hertz. 

1898. 

War  between  Spain  and 

1858. 

Atlantic  Cable. 

the  United  States. 

1859-1860. 

Spectroscope. 

1899. 

Boer    War    in    South 

1859- 

Arrhenius. 

Africa. 

1859. 

Origin  of  Species. 

1900. 

Boxer      Uprising      in 

1868. 

Antiseptic  Surgery. 

China. 

1876. 

Germ  Theory. 

Telephone. 

1877. 

Phonograph. 

1896. 

First        Successful 

Flight  (Langley). 

A  SHORT  LIST  OF  REFERENCE  BOOKS 


Particular  attention  may  be  called  to  the  important  and  valuable  publica- 
tions of  the  John  Crerar  Library,  Chicago,  prepared  by  Aksel  G.  S.  Josephson : 
viz.  A  List  of  Books  on  the  History  of  Science  (1911);  Supplement  to  the  Same 
(1916);  and  A  List  of  Books  on  the  History  of  Industry  and  Industrial  Arts 
(1915). 

A.   GENERAL 


Abelson,  Paul. 
Arago,  F.  E. 

Avebury. 
Bacon,  Francis. 
Bacon,  Roger. 
Bury,  J.  B. 
Dannemann,  F. 


Draper,  J.  W. 


Griffiths,  A.  B. 
Henderson,  L.  J. 
Holland,  R.  S. 
Hume,  M. 
Huxley,  T.  H. 

Isis. 


The   Seven   Liberal   Arts.     A   study   in 

medieval  culture. 
Biographies   of   Distinguished   Scientific 

Men. 

(See  Lubbock.) 

The  Advancement  of  Learning. 
(See  Little.) 

A  History  of  Freedom  of  Thought. 
Die    Naturwissenschaften    in    ihrer   Ent- 

wickelung    und   in    ihrem    Zusammen- 

hange.    4  vols.     (1910-1913.) 
A  us  der  Werkstatt  grosser  Forscher. 
History  of  the  Conflict  between  Religion 

and  Science. 
History  of  the  Intellectual  Development 

of  Europe. 

Biographies  of  Scientific  Men. 
The  Order  of  Nature. 
Historic  Inventions. 
The  Spanish  People. 
Advance  of  Science  in  the  Last  Half 

Century. 
Revue  consacree  a  I'histoire  de  la  science. 

(March  1913-June  1914.)     Edited  by 

G.  Sarton. 
459 


460 


A  SHORT  HISTORY  OF  SCIENCE 


Ker,  W.  P. 
Lee,  Sidney. 

V/Libby,  W. 
Little,  A.  G. 
Lubbock,  J. 
Merz,  J.  T. 

Nineteenth  Century,  The. 


Ostwald,  W.  F. 
Ostwald,  W.  F.,  Editor. 


Pearson,  K. 
Phillips,  L.  March. 
Picard,  Emile. 
Putnam,  G.  H. 

Rashdall,  H. 
Rolt-Wheeler,  F.  W. 
Routledge,  R. 
Sarton,  G. 
Schaff,  P. 
Smiles,  Samuel. 
Symonds,  J.  A. 

Thomson,  J.  A. 
Vernon-Harcourt,  L.  F. 

Wallace,  A.  R. 
Walsh,  J.  J. 


Whewell,  W. 


The  Dark  Ages. 

Great  Englishmen  of  the  Sixteenth  Cen- 
tury. 

Introduction  to  the  History  of  Science. 

Roger  Bacon,  Commemoration  Essays. 

Fifty  Years  of  Science. 

A  History  of  European  Thought  in  the 
Nineteenth  Century. 

A  review  of  progress  during  the  past  one 
hundred  years  in  the  chief  departments 
of  human  activity. 

Grosse  Manner. 

Klassiker  der  Exacten  Wissenschaften  (con- 
tains many  volumes  of  historical  in- 
terest). 

The  Grammar  of  Science. 

In  the  Desert.  » 

La  science  moderne  et  son  6tat  actuel. 

Books  and  their  Makers  during  the 
Middle  Ages. 

Universities  of  Europe  in  the  Middle  Ages. 

The  Science-History  of  the  Universe. 

A  Popular  History  of  Science. 

(See  p.  459.) 

The  Renaissance. 

Lives  of  the  Engineers. 

Renaissance  in  Italy.  The  Revival  of 
Learning. 

Progress  of  Science  in  the  Century. 

Achievements  in  Engineering  during  the 
Last  Half  Century. 

The  Wonderful  Century. 

Catholic  Churchmen  in  Science. 

The  Popes  and  Science. 

The  Thirteenth,  Greatest  of  Centuries. 

History  of  the  Inductive  Sciences,  from  the 
Earliest  to  the  Present  Times.  (1837.) 

The  Philosophy  of  the  Inductive  Sciences, 
founded  upon  their  history.  (1847.) 


A  SHORT  LIST  OF  REFERENCE  BOOKS 


461 


Whewell,  W. 


White,  A.  D. 
Williams,  H.  S. 


History  of  Scientific  Ideas.  Being  the 
first  part  of  the  philosophy  of  the  induc- 
tive sciences.  (1858.) 

A  History  of  the  Warfare  of  Science  with 
Theology  in  Christendom. 

A  History  of  Science. 

Nineteenth  Century  Science. 


Allman,  G.  J. 
Apollonius  of  Perga. 
Aristotle. 

Baikie,  James. 
Breasted,  J.  H. 

Butcher,  S.  H. 

Davidson,  Thomas. 

Euclid. 

Fairbanks,  A. 

Freeman,  K.  E. 

Frontinus. 

Galen. 

Gibbon,  Edward. 

Gomperz,  Theodor. 

Gow,  James. 
Grote,  George. 

Hawes,  C.  H.  and  H. 
Heath,  Thomas  L. 


Jastrow,  M. 
Lewes,  G.  H. 


B.   ANCIENT  SCIENCE 

Greek  Geometry  from  Thales  to  Euclid. 
Treatise  on  Conic  Sections,  (c.  220  B.C.) 
On  the  Parts  of  Animals ;  on  Generation, 

etc. 

Sea  Kings  of  Crete. 
Ancient  Times :    a  history  of  the  early 

world. 

Some  Aspects  of  the  Greek  Genius. 
Aristotle  and  Ancient  Educational  Ideals. 
Elements,     (c.  300  B.C.) 
First  Philosophers  of  Greece. 
Schools  of  Hellas. 

The  Waterworks  of  Rome.     (c.  100  A.D.) 
On  the  Natural  Faculties,     (c.  180  A.D.) 
Decline  and  Fall  of  the  Roman  Empire. 
Greek   Thinkers :    a   history   of   ancient 

philosophy. 

A  Short  History  of  Greek  Mathematics. 
Plato  and  the  Other  Companions  of 

Socrates. 

Crete  the  Forerunner  of  Greece. 
Apollonius  of  Perga. 
Archimedes. 
Aristarchus  of  Samos. 
The  Thirteen  Books  of  Euclid's  Elements. 
Diophantus  of  Alexandria. 
The  Civilization  of  Babylonia  and  Assyria. 
Aristotle;    a  Chapter  in  the  History  of 

Science. 


462 


A  SHORT  HISTORY  OF  SCIENCE 


Lubbock,  John. 
Lucretius. 
Mahaffy,  J.  P. 


Osborn,  H.  F. 
Pliny. 
Ptolemy. 
Seneca. 

Strabo. 

Tannery,  Paul. 
Walden,  J.  W.  H. 


Prehistoric  Times. 

On  the  Nature  of  Things,     (c.  90  B.C.) 

What  have  the  Greeks  done  for  Modern 

Civilization  ? 
Alexander's  Empire. 
Men  of  the  Old  Stone  Age. 
Natural  History,     (c.  70  A.D.) 
Almagest,     (c.  150  A.D.) 
Physical  Science  in  the  Time  of   Nero. 

(c.  30  A.D.) 

Geography,     (c.  10  A.D.) 
La  Geometric  Grecque. 
The  Universities  of  Ancient  Greece. 


C.  MATHEMATICAL  SCIENCE 
(Mathematics,  Astronomy,  Mechanics) 

Arthur,  James.  Time  and  its  Measurement. 

Ball,  R.  S.  Great  Astronomers. 

Ball,  W.  W.  R.  A  Primer  of  the  History  of  Mathematics. 

A  Short  Account  of  the  History  of  Mathe- 
matics. 

A  Short  History  of  Astronomy. 

Zeitschrift  fur  Geschichte  der  mathemati- 
schen  Wissenschaften. 

Martyrs  of  Science. 

Memoirs  of  Sir  Isaac  Newton. 

A  History  of  Astronomy. 

A  History  of  Elementary  Mathematics. 

A  History  of  Mathematics. 

A  History  of  the  Logarithmic  Slide-rule 
and  Allied  Instruments. 

The   Teaching   and  History  of  Mathe- 
matics in  the  United  States. 

Vorlesungen  uber  Geschichte  der  Mathe- 
matik.    Vols.  I-IV.     (1892-1898.) 

Apercu   historique  sur  Vorigine  et  le  de- 
veloppement  des  methodes  en  geometrie. 


Berry,  Arthur. 
Bibliotheca  Mathematica. 

Brewster,  David. 

Bryant,  W.  W. 
Cajori,  Florian. 


Cantor,  Moritz. 
Chaslea,  Michel. 


A  SHORT  LIST  OF  REFERENCE  BOOKS 


463 


Clerke,  A.  M. 


de  Morgan,  Augustus. 
Descartes,  Rene. 
Dreyer,  J.  L.  E. 


Duhem,  Pierre. 
Enriques,  F. 
Fink,  Karl. 
Forbes,  George. 
Galileo,  G. 


Grant,  Robert. 


Haldane,  E.  S. 
Hale,  G.  E. 
Hobson,  E.  W. 

Lockyer,  J.  N. 


Lodge,  Oliver. 
Mach,  Ernst. 


Miller,  G.  A. 

Morley,  Henry. 
Napier,  John. 
Newton,  Isaac. 

Pierpont,  James. 
Poincare,  H. 


A  Popular  History  of  Astronomy  during 

the  Nineteenth  Century. 
The  Herschels  and  Modern  Astronomy. 
Modern  Cosmogonies. 
A  Budget  of  Paradoxes. 
A  Discourse  on  Method,  etc.     (1637.) 
Tycho  Brahe. 
History  of  Planetary  Systems  from  Thales 

to  Kepler. 

Les  origines  de  la  statique. 
Problems  of  Science. 
A  Brief  History  of  Mathematics. 
History  of  Astronomy. 
Dialogues  concerning  Two  New  Sciences, 

(1638)  translated  by  H.  Crew  and  A. 

de  Salvio. 
History  of  Physical  Astronomy,  from  the 

earliest    ages    to    the   middle   of   the 

nineteenth  century. 
Descartes,  His  Life  and  Times. 
The  Study  of  Stellar  Evolution. 
"  Squaring  the  Circle."     A  History  of  the 

Problem. 
The  Dawn  of  Astronomy.     A  Study  of 

the  Temple  Worship  and  Mythology 

of  the  Ancient  Egyptians. 
Pioneers  of  Science. 
The  Science  of  Mechanics.     A  Critical 

and  Historical  Exposition  of  its  Prin- 
ciples. 
Historical  Introduction  to  Mathematical 

Literature. 
Jerome  Cardan. 

Tercentenary  Memorial  Volume. 
Philosophies   naturalis    principia    maihe- 

matica.     (1687.) 
The    History    of    Mathematics    in    the 

Nineteenth  Century. 
Science  and  Hypothesis. 


464  A  SHORT  HISTORY  OF  SCIENCE 

Poincare*,  H.  The  Value  of  Science. 

Reeves,  E.  Maps  and  Map  Making.     Three  lectures 

delivered  under  the  auspices  of  the 
Royal  Geographical  Society. 

Smith,  D.  E.  Rara  Arithmetica.     A  catalogue  of  the 

arithmetics    written    before    the    year 
MDCI  with  a  description  of  those  in 
the  library  of  George  Arthur  Plimpton 
of  New  York. 
History  of  Modern  Mathematics. 

Todhunter,  I.  History  of  the  Mathematical  Theories  of 

Attraction  and  the  Figure  of  the  Earth 
from  the  Time  of  Newton  to  that  of 
Laplace. 

A  History  of  the  Theory  of  Elasticity  and 
of  the  Strength  of  Materials,  from 
Galileo  to  Present  Time. 
A  History  of  the  Mathematical  Theory  of 
Probability  from  the  Time  of  Pascal  to 
that  of  Laplace. 


D.  PHYSICAL  AND  CHEMICAL  SCIENCE 

Armitage,  F.  P.  A  History  of  Chemistry. 

Arrhenius,  S.  A.  Theories  of  Chemistry,  being  lectures 

delivered  at  the  University  of  Cali- 
fornia. 

Barus,  Carl.  The  Progress  of  Physics  in  the  Nineteenth 

Century. 

Bauer,  Hugo.  A  History  of  Chemistry. 

Berry,  A.  J.  The  Atmosphere. 

Boyle,  Robert.  Sceptical  Chymist.     (1660.) 

Cajori,  Florian.  A  History  of  Physics  in  its  Elementary 

Branches,  including  the  Evolution  of 
Physical  Laboratories. 

Clarke,  F.  W.  The  Progress  and  Development  of  Chem- 

istry during  the  Nineteenth  Century. 

Fahie,  J.  J.  Galileo,  His  Life  and  Work. 


A  SHORT  LIST  OF  REFERENCE  BOOKS 


465 


Gilbert,  W. 
Glazebrook,  R.  T. 

Gray,  A. 
Hales,  S. 
Hilditch,  T. 
Jones,  Bence. 
Jones,  H.  C. 


Kelvin. 
Lodge,  Oliver. 


Mach,  Ernst. 

Mendenhall,  T.  C. 
Meyer,  Ernst. 

Muir,  M.  M.  Pattison. 


O'Reilly,  M.  F. 

(Potamian). 
Priestley,  Joseph. 


Ramsay,  William. 
Ramsay,  William. 

Redgrove,  H.  S. 
Roberts,  E. 
Schorlemmer,  Carl. 

Tait,  P.  G. 

Thomson,  William. 
2n 


On  the  Loadstone  and  Magnetic  Bodies, 

and  on  the  Great  Magnet,  the  Earth. 
James    Clerke    Maxwell    and    Modern 

Physics. 
Lord  Kelvin. 

Haemostatics,  etc.     (1733). 
A  Concise  History  of  Chemistry. 
Life  and  Letters  of  Faraday. 
A  New  Era  in  Chemistry ;    some  of  the 

more     important     developments     in 

General    Chemistry    during    the    last 

quarter  of  a  century. 
(See  Thomson.) 
Signalling  through  Space  without  Wires. 

Being  a  Description  of  the  Work  of 

Hertz  and  His  Successors. 
History  and  Root  of  the  Principle  of  the 

Conservation  of  Energy. 
A  Century  of  Electricity. 
A  History  of  Chemistry  from  Earliest 

Times  to  the  Present  Day. 
A  History  of  Chemical  Theories  and  Laws. 
The  Story  of  Alchemy  and  the  Beginnings 

of  Chemistry. 
Makers  of  Electricity. 

Experiments  and  Observations  on  Differ- 
ent Kinds  of  Air;  On  the  Generation 
of  Air  from  Water,  etc. 

Essays  Biographical  and  Chemical. 

The  Gases  of  the  Atmosphere.  The 
history  of  their  discovery. 

Alchemy :  Ancient  and  Modern. 

Famous  Chemists. 

The  Rise  and  Development  of  Organic 
Chemistry. 

Lectures  on  Some  Recent  Advances  in 
Physical  Science. 

Popular  Lectures  and  Addresses. 


466 


A  SHORT  HISTORY  OP  SCIENCE 


Thorpe,  T.  E. 

Tyndall,  John. 
Venable,  F.  P. 

Whetham,  W.  C.  D. 
Whittaker,  E.  T. 


Essays  in  Historical  Chemistry. 

History  of  Chemistry. 

Faraday  as  a  Discoverer. 

The  Development  of  the  Periodic  Law. 

A  Short  History  of  Chemistry. 

The  Recent  Development  of  Physical 
Science. 

A  History  of  the  Theories  of  ^Ether  and 
Electricity  from  the  Age  of  Descartes 
to  the  Close  of  the  Nineteenth  Century. 


Agassiz,  E.  C. 
Allbutt,  T.  C. 

Buck,  A.  H. 
\J    Buckley,  A.  B. 

Clodd,  Edward. 

Darwin,  Francis. 
Duncan,  P.  M. 

Foster,  Michael. 


Garrison,  F.  H. 
Geikie,  Archibald. 
Goode,  G.  Brown. 

Green,  E.  L. 
Green,  J.  R. 


E.  NATURAL  SCIENCE 
(See  also  p.  398) 

Louis  Agassiz,  His  Life  and  Correspond- 
ence. 

The  Historical  Relations  of  Medicine  and 
Surgery  to  the  End  of  the  Sixteenth 
Century. 

The  Growth  of  Medicine  to  the  Nine- 
teenth Century. 

A  Short  History  of  Natural  Science  and 
of  the  Progress  of  Discovery  from  the 
Time  of  the  Greeks  to  the  Present  Day. 

Pioneers  of  Evolution  from  Thales  to 
Huxley. 

Life  of  Charles  Darwin. 

Heroes  of  Science.  Botanists,  Zoolo- 
gists and  Geologists. 

Lectures  on  the  History  of  Physiology 
during  the  Seventeenth  and  Eighteenth 
Centuries. 

Introduction  to  the  History  of  Medicine. 

The  Founders  of  Geology. 

The  Beginnings  of  Natural  History  in 
America. 

Landmarks  of  Botanical  History. 

A  History  of  Botany. 


A  SHORT  LIST  OF  REFERENCE  BOOKS 


467 


Haddon,  A.  C. 
Harvey,  William. 


Huxley,  Leonard. 
Huxley,  T.  H. 

Judd,  J.  W. 
Lankester,  E.  R. 
Locy,  W.  A. 
Lull,  R.  S. 
Osborn,  H.  F. 


Osier,  William. 

Paget,  Stephen. 
Park,  Roswell. 
Payne,  J.  F. 
Power,  D'Arcy. 
Romanes,  G.  J. 
Sachs,  J 
Thomson,  J.  A. 


Vallery-Radot,  R. 
Woodward,  H.  B. 
Zittel,  K.  A.  von. 


History  of  Anthropology. 

An   Anatomical   Dissertation   upon   the 

Movement  of  the  Heart  and  the  Blood 

in  Animals.     (1628). 
Life    and    Letters    of    Thomas    Henry 

Huxley. 

Man's  Place  in  Nature.     Essays. 
Advance  of  Science  in  Last  Half  Century. 
The  Coming  of  Evolution. 
History  and  Scope  of  Zoology. 
Biology  and  Its  Makers. 
Organic  Evolution. 
From  the  Greeks  to  Darwin.     An  outline 

of   the  development  of  the  evolution 

idea. 

The  Origin  and  Evolution  of  Life. 
The  Growth  of  Truth  as  illustrated  in  the 

discovery  of  the  circulation  of  the  blood. 
Pasteur  and  After  Pasteur. 
An  Epitome  of  the  History  of  Medicine. 
Thomas  Sydenham. 
William  Harvey. 
Darwin  and  After  Darwin. 
History  of  Botany. 
The  Science  of  Life.     An  outline  of  the 

history    of    biology    and    its    recent 

advances. 
Life  of  Pasteur. 
History  of  Geology. 
History  of  Geology  and  Palaeontology  to 

the  End  of  the  Nineteenth  Century. 


INDEX 


Abacus,  31,  41,  147,  155,  184 
Academies,  269,  301 
Accademia  dei  Lincei,  229,  269 
Acceleration,  246,  326 
Adams,  341 
Agassiz,  373,  385 
Agricola,  226 
Agriculture,  167,  447 
Ahmes  Papyrus,  30 
Air-pump,  257,  267 
Albertus  Magnus,  177,  179 
^-Alchemy,  166,  170,  181,  187,  226,  260 
Alcmseon,  56,  63 
Alcuin,  153 
Alexandria,  87 
Algebra,  100, 133,  156, 162,  179,  232,  240, 

277,  327 
Al  Hazen,  163 
Alkarismi,  162 
Almagest,  127,  193 
Ampere,  354,  363 
Anaesthesia,  444 
Aniline,  446 

Analytic  Geometry,  110,  273,  277,  282 
Analytic  Method,  71 
Anatomy,  113,  226,  319,  373,  390 
Anaxagoras,  60 
Anaximander,  47 
Anaximenes,  48 
Animatism,  5 
Animism,  5 
Anthropology,  3 
Antiphon,  67 
Antipodes,  150,  180 
Antiquity  of  Man,  1,  387,  390 
Antiseptic  Surgery,  379 
Apollonius,  108-112,  115,  241,  303 
Arabic  Numerals,  159,  ,161,  176,  182,  184 
Arabic  Science,  156,  160-171,  176 
Archimedes,  95-107,  111,  112,  115 
Architecture,  Roman,  142,  143 
Archytas,  75,  105 
Aristarchus,  116 
Aristillus,  119 
Aristotle,  37,  45,  48,  55,  66,   74,  79-84, 

156,  172,  177,  265 
Arithmetic,  Babylonian,  26 

Greek,  40,  50,  125 

Roman,  147 


Arkwright,  441 

Arrhenius,  365 

Art,  Geometry  in,  230,  234 

Arts,  Seven  Liberal,  148,  174 

Aryabhata,  157,  160 

Assyria  (see  Babylonia) 

Astrolabe,  127,  129 

Astrology,  23,  132,  181,  204,  210,  253 

Astronomy,  Babylonian,  27 

primitive,  21 

Atmosphere,  256,  260,  307,  315 
Atomism,  61,  348,  361 
Attraction,  293,  348 
Augustine,  St.,  150 
Avogadro,  362 

Babylonia,  2,  7-11,  26-29,  36,  43,  139 

Bacon,  Francis,  81,  203,  270,  312 

Bacon,  Roger,  177,  180,  400 

Bacteriology,  380 

Baer,  von,  375,  393 

Balance,  258,  308 

Barometer,  256,  267,  302 

Barrow,  289 

Becher,  262 

Bell,  445 

Bergmann,  305 

Berkeley,  298 

Bernard,  376 

Bernoulli,  326 

Bessel,  344 

Bessemer,  446 

Bhaskara,  158 

Biogenesis,  381 

Biology,  315,  371,  392 

Black,  305,  312 

Black  Death,  185 

Blood,  Circulation  of,  255,  412 

Boerhaave,  263 

Boethius,  148,  153,  182 

Bonnet,  320,  372 

Botany,  315,  317,  371,  374 

Boyle,  258,  260-262,  334 

Brahmagupta,  157,  160,  162 

Briggs,  244 

Brown,  393 

Brunelleschi,  234 

Bruno,  254 

Bryson,  67 


469 


470 


INDEX 


Buffon,  318,  335,  372,  386 
Bunsen,  353 
Biirgi,  244,  252 

Csesar,  143 

Cajculus,  96,  99,  112,  147,  253,  273,  279, 

282,  296,  324 

Calendar,  21,  29,  38,  143,  181,  242 
Calippus,  78 
Caloric,  265,  312 
Calorimetry,  312 
Candolle,  de,  374 
Canopus,  Decree  of,  108 
Capella,  M.,  147 
Carbon,  309 

Carbonic  Acid  Gas,  305,  309 
Cardan,  239 
Carnot,  350 
Catastrophism,  383 
Cavalieri,  278-280 
Cave  Animals,  386 
Cavendish,  306,  309 
Cell  Theory,  375,  391 
Centrifugal  Force,  288 
Chaldeans,  8 
Chambers,  369 
Charlemagne,  Schools  of,  153 
Chemistry,  226,  260,  304,  360 
Chladni,  311 
Church,  Attitude  of,  149 
Circle,    Squaring    of,    28,    32,    67,    98, 

337 

Clausius,  357,  364 
Clepsydra,  27,  40,  127,  148,  163 
Clocks,  188,  248,  266,  287,  328 
Columbus,  181,  192 
Combustion,  260,  262,  307,  309 
Comets,  83,  207,  302 
Comparative  Anatomy,  390 
Compass,  164,  187 
Computation,  41,  147,  182,  236,  242 
Computing  Machine,  285,  301 
Conic  Sections,  76,  95,  108-112,  281 
Conservation  of  Energy,  289,  348,  349, 

355,  357 
Contagion,  375 
Continuity,  79 

Coordinates,  110,  122,  125,  273,  277 
Copernicus,  55,  194-203,  339,  407 
Cosmogony,  371,  387 
Cosmology,  23,  45,  73,  77 
Cotton  Gin,  441 
Coulomb,  354 
Counting,  23-25 
Crete,  16-18 
Crusades,  172 
Crystallography,  364 
Ctesibius,  123 


Cube,  Duplication  of,  68,  71,  75,  76,  108, 

241 
Cubic   Equations,   100,    135,   163,   179, 

239 

Cuneiform  Writing,  9 
Cusa,  Nicholas  of,  192 
Cuvier,  372,  386 

d'Alembert,  328 

Dalton,  361 

Dante,  181 

Dark  Ages,  141,  152 

Darwin,  367,  393,  394-396 

Davy,  364 

Decimal  Fractions,  252 

Decimal  System,  159,  178 

Degrees,  29 

Delia  Porta,  228,  269 

Democritus,  33,  46,  48,  61,  62,  77 

Desargues,  280 

Descartes,     111,    265,    270,    271,    273- 

280 

Descent  of  Man,  395 
De  Vries,  396 
Dinostratus,  65 
Diophantus,  133-138,  276,  282 
Disease,  264 

Dissipation  of  Energy,  358 
Dissociation,  electrolytic,  365 
Division,  183 
Dufay,  314 
Diirer,  A.,  235 
Dynamics,  248,  293 
Dynamite,  439 

Earth,  Motion  of,  54,  85,  116,  128,  192, 

195 

Size  of,  82,  107,  163,  199 
Eclipses,  10,  28,  30,  43,  55,  121,  129 
Ecliptic,  55,  108,  129 
Economy  of  Nature,  282,  283,  390 
Egypt,  11,  29-34,  36,  43,  45,  49,  139 
Elasticity,  346 
Electricity,  313,  354,  445 
Electric  Lighting,  446 
Electrolysis,  364 

Electromagnetic  Theory  of  Light,  355 
Elements,    45,  47,  52,  59,   74,    83,  261, 

315,  363 

Ellipse,  99,  110,  279,  280 
Embryology,  256,  375 
Empedocles,  59 

Energy,  348,  349,  355,  357,  358 
Engineering,  104,  123,  142,  321,  447 
Epicurus,  84 

Epicycles,  118,  129,  199,  212 
Epigenesis,  375 
Equant,  129,  199 


INDEX 


471 


Equations,  Theory  of,  241,  277,  296 
Equinoxes,  Precession  of,  120,  129,  165, 

199 

Erasistratus,  113 
Eratosthenes,  107,  122 
Ether,  286,  356 

Euclid,  88-95,  97,  110,  134,  173 
Eudemus,  38,  42 
Eudoxus,  77,  88,  90,  105,  119 
Euler,  283,  326 
Eustachius,  227 
Evolution,  225,  317,  322,  343,  349,  366, 

388,  395 

Excentric  Orbits,  117,  129 
Exhaustion,  Method  of,  77,  112 
Experimentation,  259 
Explosives,  440 

Fabricius,  227,  255 

Falling  Bodies,  80,  239,  246 

Fallopius,  227 

Faraday,  354,  364 

Fermat,  110,  282,  301 

Fermentation,  258,  378 

Ferrari,  239 

Fibonacci,  177,  178 

Finger  Reckoning,  147,  182 

Fizeau,  352 

Fluids,  249,  289.    (See  also  Hydrostatics) 

Fluxions,  296,  326 

Food  Preservation,  446 

Fossils,  56,  228,  316,  317,  385 

Foucault,  352 

Fractions,  30,  135,  163 

Frankland,  362 

Franklin,  270,  314,  329 

Fraunhofer,  353 

Fresnel,  351 

Frontinus,  144 

Function,  243,  324,  327,  336 

Galen,  113,  142,  146 

Galileo,  63,  217-226,  230,  245-253,  267, 

310,  414 

Galvani,  314,  321 
Gas,  258,  305,  321,  443 
Gauss,  323,  337,  340 
Geminus,  38,  85,  97 
Geography,  107,  132,  145,  181 
Geology,  315,  371,  383 
Geometry,  Egyptian,  32,  33 

primitive,  25 
Gerbert,  155 
Germ  Theory,  378 
Gesner,  228,  386 
Gilbert,  228,  313 
Gioja,  187 
Glaciers,  385 


Goethe,  374 

Gravitation,  214,  291-295,  342 

Gray,  314 

Greek  Science,  35,  59,  131,  139 

Green,  345,  354 

Grew,  268 

Guericke,  257,  313 

Gunpowder,  164,  439 

Gutenberg,  189 

Hales,  263,  268,  305,  335 

Haller,  319 

Halley,  296,  302 

Hargreaves,  441 

Harriott,  245 

Harvey,  255,  264,  271,  375,  412 

Hawksbee,  311,  313 

Heat,  249,  312,  350 

Hebrews,  16 

Helmholtz,  311,  323,  356-359,  439,  444 

Helmont,  Van,  258 

Heraclides,  85 

Hero,  123 

Herodotus,  16 

Herophilus,  113 

Herschel,  333 

Hertz,  356 

Hicetas,  54,  56 

Hindu  Science,  156-160 

Hipparchus,  119-123,  126,  129,  131 

Hippias,  65 

Hippocrates  of  Chios,  67,  90    • 

Hippocrates  of  Cos,  63,  113,  377 

Oath  of,  399 
Hooke,  268,  316 
Hour,  28,  40 
Huggins,  353 
Humanism,  185,  191 
Humboldt,  von,  393 
Hunter,  319 
Hutton,  317,  383 
Huxley,  269,  366,  372 
Huygens,  266,  286 
Hydrogen,  306,  309 
Hydrostatics,  103,  249,  252 
Hypatia,  138 
Hypsicles,  115 

Impact,  288,  290 

Incommensurables,  89 

India-rubber,  444 

Indivisibles,  278,  297 

Industrial  Revolution,  320,  367 

Infinitesimals,  66,  78,  299,  326 

Infinity,  159,  251 

Integration,  280,  289 

Internal  Combustion  Engines,  446 

Inventions,  123,  189,  320,  396,  438-448 


472 


INDEX 


Ionian  Philosophers,  42 

Ions,  364 

Irrational  Numbers,  52,  101,  290 

Janssen,  354 
Jenner,  322,  422 
Jordanus  nemorarius,  179 
Joule,  349,  351,  357 
Jupiter,  Satellites  of,  221 
Jussieu,  de,  318,  374 
Justinian,  Edict  of,  152 

Kelvin  (see  Thomson) 

Kepler,  208,  210-217,  222,  245,  279 

Kinetic  Theory  of  Gases,  357 

Kircher,  264,  267 

Kirchhoff,  353 

Koch,  380 

Laboratories,  360 

Lactantius,  149 

Lagrange,  251,  273,  328-330,  336 

Lamarck,  372,  386,  392 

Laplace,  330 

Lavoisier,  308,  360 

Leap-year,  30,  79,  108 

Leeuwenhoek,  264,  268 

Leibnitz,  299 

Lenses,  163,  265,  302,  313 

Leonardo  da  Vinci,  228,  234,  252 

Leucippus,  61,  62 

Lever,  80,  102,  123 

Leverrier,  341 

Liebig,  260,  360 

Light,  313,  327,  351,  355 

Velocity  of,  216,  250,  286,  351 
Limit,  78,  112,  253 
Linnaeus,  318,  372,  374 
Lister,  379 
Lobatchewski,  338 
Lockyer,  354 
Locomotive,  442 
Locus  of  Equation,  277 
Logarithms,  215,  230,  242 
Lucretius,  144 
Ludolph  von  Ceulen,  245 
Lyell,  317,  384,  394,  429 

Maclaurin,  326 

Magnetic  Charts,  303 

Magnetism,  228,  313,  354 

Malpighi,  256,  268,  319 

Malthus,  390 

Manometer,  266,  268 

Maps,  25,  48,  132,  143,  192,  241,  303 

Margarita  philosophica,  235 

Maxwell,  354,  356,  357 

Mayer,  349,  357 


Mayow,  260 

Mechanics,  80,  102,  123,  133,  214,"  218, 

219,   230,    234,    245-252,    286-289, 

328,  330,  346 
Medicine,  56,  63,  113,  144,  166,  226,  263, 

322 

Mensechmus,  76 
Mendel,  396 
Mendelejeff,  363 
Mercator,  241 
Metallurgy,  226 
Meton,  39 
Micrometer,  267 
Microscope,  267 

compound,  319,  374,  442 
Middle  Ages,  151 
Milky  Way,  61,  63,  179,  222 
Mineralogy,  226 
Molecules,  361 
Moment  of  Inertia,  288 
Monge,  282,  335 
Month,  22,  38 

Moorish  Science,  156,  165,  176 
Moro,  317 

Mortality  Statistics,  303 
Motion,  Laws  of,  246,  290,  293 
Miiller,  376 
Multiplication,  31,  182 

Napier,  242 

Natural  History,  146,  227,  315,  370 

Natural  Selection,  395 

Natural  Theology,  369 

Navigation,  192,  193 

Nebular  Hypothesis,  278,  331,  343 

Negative  Numbers,  159 

Neptune,  341 

Newcomen,  312,  440 

Newton,  290-301,  420 

Nicomachus,  125 

Nitrogen,  306 

Nitro-glycerine,  439 

Non-Euclidian  Geometry,  91,  337 

Number  Theory,  41,  50,  72,  89,  125,  282 

Numbers,  Imaginary,  340 

Oersted,  354 

Ophthalmoscope,  444 

Optics,  95,  124,  132,  163,  215,  264,  286, 

291,  302 

Organic  Chemistry,  263 
Origin  of  Species,  369,  394 
Oxygen,  260,  307,  309 
Oughtred,  245 

Pacioli,  232 
Palaeontology,  385 
Palissy,  228 


INDEX 


473 


Pappus,  38,  110,  132,  276,  277 

Paracelsus,  226 

Parallelogram  of  Forces,  248,  253 

Parasitology,  378,  380 

Parmenides,  59 

Pascal,  257,  282 

Pasteur,  377-382 

Pathology,  264,  377 

Pendulum,  163,  219,  248,  266,  287 

Periodic  Law,  363 

Perspective,  61,  235 

Perturbation,  295,  331,  342 

Petrarch,  186 

Peurbach,  193 

Philolaus,  54 

Phlogiston,  262,  305 

Phoenicians,  13-16,  43 

Photography,  444 

Physical  Chemistry,  364 

Physics,  Modern,  350 

Physiologus,  175 

Physiology,  319,  376 

Pisano,  Leonardo  (see  Fibonacci) 

Planets,  22 

Plato,  58,  69,  105 

Pliny,  146 

Pneumatics,  123 

Poincare,  339 

Polyhedra,  regular,  51,  89,  90,  211 

Poncelet,  357 

Posidonius,  108,  147 

Power,  320,  439 

Priestley,  306,  309 

Prime  Numbers,  89,  108 

Principia,  292,  420 

Printing,  189 

Probability,  282,  283,  284,  332 

Proclus,  38,  88,  90,  92,  119 

Projection,  122,  132,  242 

Projective  Geometry,  280 

Protoplasm,  375,  391 

Ptolemy,  Il9,  126,  138,  176 

Pumps,  246,  257 

Pyramids,  29,  32,  44 

Pythagoras,  49,  90,  310 

Quadrants,  163,  206 

Quadratic  Equations,  65,  89,  134,  162 

Quadrivium,  50,  148,  174 

Rainbow,  292,  402 

Ramus,  210,  213 

Ray,  316,  369 

Recorde,  202,  236 

Reductio  ad  absurdum,  65,  67 

Refraction,  132,  163,  181,  215,  265,  266, 

283,  287,  292,  327 
Refrigeration,  445 


Regiomontanus,  191,  193 
Reinhold,  201 
Renaissance,  172,  185 
Retrogressions,  118 
Rheticus,  196,  241 
Romer,  266,  286 
Royal  Society,  268,  269 
Rumford,  312,  322,  350,  357 
Rutherford,  306 

Sacrobosco,  180 
St.  Hilaire,  372 

Saturn,  Rings  of,  223,  266,  286 
Sauveur,  311 
Scheele,  30.8,  334 
Scholasticism,  155,  174 
Seebeck,  354 
Seleucus,  117 
Servetus,  227 
Sewing-machine,  442 
Slide-rule,  245 
Smith,  317 
Snellius,  266 
Socrates,  69 
Sophists,  64 
Spallanzani,  320,  382 
Sound,  250,  310 
Spectroscope,  353 
Spectrum,  266,  353 
Spinning  Jenny,  441 
Spirals,  99 

Spontaneous  Generation,  381 
Stahl,  262 

Stars,  Distance  of,  116,  209,  303,  344 
Steamboat,  442 

Steam-engine,  258,  312,  320,  440 
Steel,  446 
Stevinus,  252 
Stifel,  235,  242 
Strabo,  145,  147 

Sun-dial,  28,  29,  39,  45,  134,  148 
Sydenham,  264,  377 

Symbols,  159,  184,  231,  233,  236,  237, 
240,  245,  277,  301 

Tables,  astronomical,  128,  165,  176,  193, 

201,  215 
Tartaglia,  237 
Telegraph,  445 
Telephone,  445 
Telescope,  215,  219,  229,  266,  267,  291, 

313 

Thales,  42 
Theeetetus,  70,  88 
Theon,  38,  90 
Theophrastus,  46,  47,  84 
Thermodynamics,  351,  365 
Thermometer,  249,  267 


474 


INDEX 


Thomson,  W.,  278,  341,  356,  358,  362 

Three  Bodies,  Problem  of,  331 

Tides,  117,  181 

Time  Measurement,  27,  39,  127,  207,  247 

Timocharis,  119 

Torricelli,  253,  256 

Treviranus,  371,  392 

Trigonometry,  115,  122,  128,   133,   163, 

193,  241 

Trisection  of  Angle,  29,  65,  241 
Trivium,  148,  174 
Tycho  Brahe,  203-209 
Tyndall,  311,  382 

Universities,  175,  184,  321 
Uraniborg,  206 
Uranus,  333,  342 

Vaccination,  322,  425 
Vacuum,  247,  257 
Van  t'  Hoff ,  364 
Vesalius,  226,  264 
Vieta,  240 
Vitruvius,  103,  143 
Vivisection,  113 
Vlacq,  245 


Volta,  314 
Vortices,  278 

Wall,  314 

Wallace,  367,  395 

Wallis,  269,  289 

Water,  Composition  of,  309,  316 

Watson,  314 

Watt,  312,  320,  441 

Week,  22 

Weismann,  396 

Werner,  317,  386 

Wheeler,  314 

Wohler,  363,  375,  391 

Wren,  288 

Xenocrates,  77 
Xenophanes,  56 

Year,  21,  38,  120 
Young,  351 

Zeno,  66 

Zero,  40,  159 

Zoology,  315,  317,  371,  372 

Zymology,  378 


Printed  in  the  United  Statea  of  America. 


RETURN     CIRCULATION  DEPARTMENT 


202  Main  Librar 


DUE  AS  STAMPED  BELOW 


V! 028 


[GENE/ML 


UNIVERSITY  OF  CALIFORNIA  UBRARY 


